Good evening, everyone. And thank you for joining me again. These webinar series that I've been presenting every Wednesday evening have been great. I've really enjoyed visiting with you. The last one of these will be next Wednesday. And during that webinar, we will be discussing how to get everything ready for spring, everything from a perennial flower bed to your lawn and everything in between. My name is Don Kinsler. I'm the NDSU Extension Horticulture Agent here in Cass County. And again, I'm so happy that you're joining us. We've got approximately 150 or so on with us this evening. So again, welcome. Well, let's get right into pruning. Now it's interesting. Most of us know that our trees shrubs will need pruning from time to time, but it's not always so obvious when or how we should be doing the pruning. So that's what we're going to cover tonight is we're going to cover everything from pruning apple trees all the way to pruning landscape shrubs. So we might think, well, why do we prune? You know, we don't just prune kind of because just because, of course, we prune for specific reasons. Now because one of those could be dead branches or shrubbery might have some dead branches or maybe rabbits nibbled on an apple tree branch and that branch died so we need to remove the dead wood so it doesn't harbor insects and diseases. And of course, to improve the appearance or shape, maybe we need to control the size. Maybe a shrub is growing right next to the sidewalk and it's been encroaching the sidewalk where you're trying to blow the snow away. So sometimes we need to just get things back in bounds. Now some things can be encouraged to flower better or to fruit better. For example, the yellow flowered potentilla there blooms much better if it has an occasional pruning or cutback. So we'll talk about that more later. And of course, apple trees can be encouraged to fruit better if we do the right type of pruning. And of course, if you've got a formal hedge to make a nice dense well trimmed hedge that will need pruning also. So it's fun to talk about pruning. Now the program that you're seeing this evening is brand new. This has never been presented before. I just finished it up actually today. So you are the first group that has ever seen my program on pruning in this format. So when to prune? As a general rule, when trees or shrubs are dormant in late winter or early spring, that's the time to prune most things. And there's a reason for that. If we wait until things have leafed out in the springtime, such as May or June, if we wait at that time, the tree or shrub has wasted energy producing leaves and buds, maybe flowers that we just cut off. So it's wasted a lot of energy. Instead, if we do that pruning, well, the shrubs are still dormant before they leaf out, all the new energy can go into new growth. So the timing is usually, of course, it varies by the year, but the timing is usually maybe sometime early April. We can just watch, you know, after the snow kind of tends to disappear. But before the new buds start to open up, that's the general time for most things that they would be pruned. There are a couple of exceptions, of course. And now these exceptions are what maples and birch are a classic example of the exception. Maples and birch both have sap that bleeds quite easily from pruning wounds. And if we prune them too early in the spring, there's a bunch of sap that oozes out. It doesn't actually hurt the trees, but it looks really, really bad coming down on the trunks of trees. And so both maples and birch should be delayed in pruning until after they have leafed out. After they've leafed out, the leaves are probably full-size. Then you could go ahead and do some pruning on those and the sap won't run out of the wounds. Another exception to the pruning rule, the exception to the rule where you prune when things are dormant, is spring flowering shrubs. Now I show two of those here. One is the yellow-flowered fursithia and the other is lilac. And of course they bloom in very early spring. So if we did pruning during the dormant time, you know, right before spring, we would be cutting off a lot of flower buds that were due to open up.  And they're ready to burst forth as soon as the weather cooperates. You see, so if we do much pruning in late winter early spring, we're cutting off a good share of the flowers. So anyway, on spring flowering shrubs like fursithia, lilac, they can be delayed pruning until after you've enjoyed the blossoming and then go ahead and prune. I don't want to wait too much into the summer though because then they won't set up next year's flower buds. So right away after pruning, after flowering for fursithia, lilac, and other spring blooming shrubs. Now here's a question I oftentimes get. Sometimes in the fall of the year, maybe September, October, people will contact me and say, you know, I just, I didn't get my fall pruning done. Is it okay to do it next spring? Well, actually, there's not a good reason to prune in the fall. And there's quite a few bad reasons to prune in the fall. Now here's the concept. Trees and shrubs are very smart. They know in late summer and fall, they know that winter is coming. So in response to shorter days and cooler temperatures, they start to slow growth in preparation for wintertime. And part of that slowed growth is slowed cell division, you know, in the cells within the branches. So if we do pruning cuts in the fall, those pruning wounds do not heal themselves or seal themselves over the way they do earlier. Because the reason they don't seal themselves over is because the trees and shrubs have slowed down that cell growth and cell division. So the pruning cuts remain open. They remain open and unhealed throughout the fall and winter. So there's a greater chance of getting branch dieback during winter if you prune in the fall of the year. Now, it doesn't automatically mean if you did fall prune, it doesn't mean things are going to die. But it increases the chance of something going wrong. And there's really no good reason. There's no benefit to fall pruning. So really, we should wait until spring, you know, unless there's a really good reason. For example, if the shrub is sticking over the sidewalk and you're going to need to get by it with the snowblower, certainly go ahead and trim. But generally, there's not a good reason to prune in the fall and it can be a little risky. Deadwood can be pruned out anytime. Anytime that we see through the course of the growing season, if we see deadwood, that should be cut back, back to the point at which that deadwood originated. The reason for that is because deadwood can harbor insects and diseases. So that should be gotten out anytime that you do see it. Now, here's an important number one rule of pruning, and that is to never leave stubs. If we look at the rose bush on the right hand side, notice how it was pruned, leaving a dead end stub. And that dead end stub has totally died back. Now, the proper spot to prune always is where there's something else at that point, at the point at which you cut. Now, it could be another branch arising, or it could just be a bud. If you take a look at the photo on the left hand side, the pruning shears, the pruning cut is going to be made where another branch is going to take over. So when that pruning cut heals, there will be something else that will take over that area.  And of course, that dead end stub is oftentimes where diseases will enter into the tree or shrub. And here we can save ourselves a lot of time and money by not buying pruning paints and pruning sealers. They're not recommended. There's been a lot of research done on this as to whether they're effective and not only aren't they effective in promoting healing, but they're actually dangerous. What they do is they put a coating over that pruning wound and that coating can seal in disease bacteria and fungi underneath that coating. There can be a light film of moisture that stays underneath. And so it's actually been shown that more diseases and problems arise if you do put the pruning paint on. Again, it doesn't mean that every cut that was treated with pruning paint is going to automatically die out of problems. But you're greatly increasing the risk of something going wrong. If you do use the sealers, instead, plants, trees, shrubs have the ability to compartmentalize that wound. If we just leave the wound exposed to the air, the cell division will take care of the rest. And now here we see a well-heeled pruning wound. Isn't that neat? The ability of a tree or shrub to compartmentalize that wound and seal it off from infections by insects, diseases, moisture won't get in. And so if we do the pruning properly and we'll kind of go over some proper techniques. But if we do it properly like that, the wound will seal or heal itself on its own. Now, what about the tools that we need? Well, there are about three, at least, that we need maybe four. So one of the most useful are the handheld pruning shears. Now, when I was a young guy kind of learning this stuff, one of my great teachers, Neil Holland, a professor at NDSU, and went on to open his own garden center for many years, he always indicated that these handheld pruning shears were for pencil-sized diameter branches. He indicated the danger of trying to do too big of a branch because that could ruin a very good pruning shears. I should mention, too, that it pays to buy the good pruning tools are going to last a lifetime. The cheap tools, the less expensive, just don't do the job as well and they can be frustrating. So invest in high-quality tools and they'll last a long time. So now the long-handled loppers shown there are generally for about a one inch to one-and-a-half inch diameter branch. They're also slick for pruning down in a shrub. We're going to talk about rejuvenation in a little bit, and that type of pruning shears, the loppers, really works well for reaching down in and getting some of the larger branches for rejuvenation. Another one, of course, for larger than about an inch and a half are pruning saws. Now, here's an interesting concept, too. Head shears, like the ladies using their head shears or the electric or gas shears, are really only for hedges, not for trimming or pruning other types of shrubbery. And we'll take a look why in a minute. So if you've got a formal type hedge, then the hedge shears, either handheld or the electric or gas, will work well. Okay, next we're going to go into some individual types of things that need pruning. So first of all is apple tree pruning. Now apple tree pruning is really, really important for a number of reasons. The main reason is a properly pruned apple tree will bear its fruit lower on the tree. Now, if left to its own devices, apple trees become large and rounded, and the outer branches are the ones that get the more sunlight. And as a result, those branches are the ones that produce the flowers on the outer perimeter of the tree. And those flowers are what turns into the fruit. So if left to its own devices, an apple tree will have most of the fruit up on the upper outside, where it's a lot more difficult to pick those apples. But if we can do the proper pruning, we'll get those fruit to form a lot lower on the tree. So the preferred shape of an apple tree is more of a pyramid, a pyramidal type shape or a Christmas tree shape, where the lower branches are the widest out, and then they taper on up, as you can see in the photo there. So it's interesting, but what this does is it allows the lower branches to catch more sunlight. They don't get shaded out. And so as a result, those lower branches will form more flower buds due to the sunshine, and then those, in turn, will give the fruit. So you'll have more fruit lower on the tree. So picking is a lot easier. So in addition to shaping the tree, I should make a few comments about shaping the tree. So on a young tree, it's fairly easy. A young tree that you've planted, maybe with the last couple of years, two, three, four years, you simply start at the bottom, the bottom branches, and then prune.  And so that's fairly easy on a young tree. What if you have an older tree, you know, that's already big and rounded? Well, those will take probably four to five years of getting them into a better shape. But if you do a little each year, then eventually you can get even an older tree kind of pruned back into a shape that's a little more manageable. So in addition to shaping it like that, there are other things in an apple tree that should be pruned. If there are any suckers down at the bottom of the tree coming out of the base at ground level, those should be pruned off. And then basically to thin out the crowded branches. By thinning out all the crowded branches, or as many crowded branches as you can see, it'll let more sunlight in, let more air in, and then you'll get more blossoming kind of in the more inside the tree, and you'll get better fruiting kind of throughout the tree. They're really, it's really not possible to overprune an apple tree. Usually we're hesitant and so we don't prune enough. There's an old saying that you should be able to take a football and throw it through the branches of an apple tree and not hit any branches. So again, I love the old pruning adage, prune until it hurts and then prune some more. And if you take a look at the apple tree, any inward facing branches, they're kind of pointing inward, or if there are a lot of little, they're called water sprouts, a lot of kind of weak shoots coming up off the branches, go ahead and prune those out. So again, I've never known anyone that has killed an apple tree by pruning too much. So again, go ahead and really thin that out. It's important, especially on the larger branches, to know the proper spot to make that cut. So if we take a look first on the left hand photos, notice where the kind of the side branch meets the main trunk. There's a ridge there isn't there where the green errors are pointing. Notice that ridge, that natural joint between the two branches or between the branch and the main. The proper pruning cut is just outside of that ridge. And there's a good reason for that. That ridge, something that's called the branch collar, that has cells in it that will heal. That's where the healing tissue, the tissue that will compartmentalize and seal off that wound. That's where that tissue is located. If we do a flush cut like way over on the right hand side, if we do a flush cut, we're pruning off those healing type cells. So it's very important to prune right outside of that branch collar, right outside of the branch ridge. So a good pruning cut would be off to the left hand side, the lower photo there. You see a branch pruned away. So sometimes we're mistakenly thinking that we should make a very flush cut, but not so. A lot of research has shown that that healing tissue is in that branch ridge. Now this holds true both for apple trees, fruit trees, and other trees as well. We'll talk about other trees in just a minute. So the timing of apple tree pruning. Now the long, long held timing of pruning has always been in late winter and early spring before they leaf out. And of course, like I mentioned before, one reason is the apple tree would waste energy leafing out and we just cut those leaves away. So it's wasted some energy. There's another reason for pruning in late winter, early spring. And that is for control of fire blight disease. Now you see in the photo here, the fire blight organism, in addition to scorching the leaves, the bacteria disease also causes a very noticeable symptom. And that is what's called the shepherd's crook type growth. Notice the way the twig has bent over just in the shape of a shepherd's crook or shepherd's hook. And so that's quite diagnostic on fire blight. And then notice at the base of that twig, the fire blight, the canker that has enlarged in that branch. So that's a quite serious infestation. It's already gone to the larger branch. So the fire blight bacteria is not active in the wintertime. And so because of that, late winter, early spring is a good time to prune apple trees if you've ever had any fire blight issues. Also speaking of pruning and disease, if you've ever had any disease on an apple tree or another tree, it's very important to dip your pruning shears, your pruning tools into a sterilizing solution in between each cut. So we don't spread any disease pathogens from one cut to another. A good product to use would be like household bleach, about nine parts water to one part bleach and dip in. Make sure you rinse your tools when you're all done pruning for the day. Make sure you rinse that hilux or that bleach off because that can be quite, quite rusting, quite caustic to tools. There is another disease, though, that affects probably more apple trees and actually is the number one killer of apple trees in North Dakota and probably Minnesota.  It almost looks like it's been sprayed with tar, doesn't it? But it hasn't. If you take a look just up above beyond that black portion, notice how the bark does not look normal and also below that black wound on the main trunk. You can notice the blackening kind of a discoloration. The apple wood should be more of a coppery color, such as you see up at the far left-hand corner. It's a little more normal. So anyway, this is black rot fungus that has entered an old pruning wound. And there is a, there's new thinking on how to prevent this, and this is a tremendously serious disease. I get lots of calls and emails on this every year. There is a new way of thinking for the timing of pruning on apple trees, especially if you've had any black rot injury on the tree. And the timing is delaying the pruning until growth has already started on the tree. And there's a reason for that. If the tree has started growth, you know, sending out some new leaves, we know that the cells are dividing. And so when we make the pruning cut, those cells will divide and seal off that pruning wound quicker. So, so there has been some kind of rethinking on the timing of apple tree pruning. Again, if there's any fire blight at all history, then absolutely prune in winter before things start leafing out and that bacteria would become active again. But if you've noticed any of this black rot blackening on an apple tree, then maybe wait with your pruning until the leaves have started to hop out a little bit. Then we know that the tree is active, grow actively growing and going to seal over that pruning wound a little. Again, it would do no good to apply pruning paint because that actually seals in the rotting bacteria. Okay, other fruit trees are pruned pretty much the same way as apple trees in that pyramidal type shape and thin out the branches so that to get better blossoming and better fruiting as well. I should mention also that we'll have time for questions at the end and at the end or when you think of them if you put them in the Q&A box that you should see down at the end, down at the lower portion or somewhere on your screen should be a Q&A spot. So pruning shade trees, now there oftentimes isn't a lot of pruning that us homeowners would be doing on a shade tree. I'm not going to climb up as that gentleman is doing, but sometimes there are different reasons why we would prune ourselves. And one of those is if the tree branches are just growing too low and we're hitting them with a lawn mower. Now I kind of like to see a low headed tree like that. It has kind of nice natural shape. But if they're in the way of things, then sometimes we do need to do some pruning of branches also. So there are certain times that it does pay to do some pruning by ourselves. These same pruning cuts that we described with when pruning apples can be done on trees as well to make sure that you make the cut just outside of that bark ridge, that circular ridge on the main trunks or main branches. That brings up a good point though. On a young tree that you might have planted over the course of the last few years or are going to plant, it's important to leave the lower branches intact for a number of years. Those lower branches are feeding the tree, the leaves and everything on those branches do their photosynthesis thing, and they help the tree to grow faster. It will increase in trunk diameter and increase in tree height better if you leave the lower branches intact for at least a few years. Now, maybe those lower branches are going to be too low. Maybe they're going to aim over a sidewalk or something. So there is oftentimes a reason for removing lower branches later. But delay after maybe four years, five years, but don't wait so long that the branches become large. Then it makes such a large pruning wound. But maybe when they're inch or so, inch and a half diameter, then go ahead and remove those lower branches, but leave them on for a few years to help feed the tree. So again, there's a well-healed pruning wound. Now let's talk about pruning evergreens. The spruce trees shown here. Now, what do you like? The spruce on the left? Now, there are marriages that have been tested with this. Some people favor taking off the lower branches on spruce trees. Others favor letting the branches sweep the ground. Some people don't like to have to mow around those. There is a compromise, though. A person can prune away some of the branches that absolutely sweep down onto the grass. You can remove just a few of those and yet leave the shape of it. You can probably tell which I favor. I do favor the natural shape of the tree on the left-hand side, but that doesn't mean it's right. So that's kind of a personal preference, but it is important to notice to note that once those branches are cut off, they aren't going to grow back again. So one wants to be really certain that you want them totally removed. And of course, I couldn't resist putting in this slide because, you know, those little spruce trees look so cute when they're small, don't they? But of course, they aren't meant to be a foundation planting. They need to be out farther from the house. So of course, there really wasn't much choice here than I supposed to cut off all the branches that were just sticking out way, way too far into the driveway. So a good case for remembering the ultimate size and diameter and height of the trees and shrubs that we plant. So on pruning evergreens, maybe you need to shape them up a little bit or maybe they've extended out a little too far and you do need to do some pruning on the sides. The pruning can be done before new growth emerges. So probably the month of May, late April into May, evergreens are somewhat flexible as to the timing that we would do the pruning. But you could prune before they start sending out their little growth tips as you see here. So spruce can be pruned really, you know, just kind of before they start that or about this time would even be fine too. There's a little bit of a window of opportunity on that, but preferably before they would start the new growth. Next, let's talk about pruning shrubs. Up to this point, we've been talking about pruning trees. But let's talk about pruning shrubs. And there's a couple of good reasons, of course, for pruning shrubs. We might need to maintain their height, their size, their shape to keep them looking good. But there's another really good reason for pruning shrubs. And that's to rejuvenate them. And we'll talk about each of these in a little more detail here. Now, when pruning to maintain the height, shape or size of a shrub, we can have a very nice natural look to that shrub.  See, rather than just kind of shearing all the way across the top, if we selectively shorten them back at a little bit of a random pattern, we still reduce the height or the width, but we do it a little more randomly by selectively cutting. That gives a nice beautiful shape such as these variegated dogwoods. Now, shearing isn't really recommended for a couple of reasons. Most shrubs have a natural beauty. And if we let that natural beauty shine through, it seems they just kind of look better and do better. So on the left-hand side, we see a shrub, a deciduous leafy type shrub that has been sheared quite tightly. And you get kind of a mass of twigginess on the outside. And of course, if you look at the Pinkflower shrub, that's another case for giving them the footprint that they need to develop, so we don't need to cut off that portion. And it's also been sheared quite heavily. So to prune shrubbery like this, in most cases, you'd be using a handheld pruning shears or a loppers, and not so much the electronic or gas-powered head shears. Or unless you live in Disney World, then there's certainly a spot for shearing, isn't there? All right, the next pruning type is to rejuvenate. Now, the wonderful thing about deciduous leafy type shrubs is that if they get old and overgrown, in most cases, we can rejuvenate them. If they become kind of bare, if the branches are old and woody and they just aren't blooming as good and just kind of don't look so good anymore, we can give them a whole new lease on life by cutting them way back. And when I say cutting way back, all the way down to about four to six inches above ground level. When I first saw this as a young boy, my mom took a saw to our lilac tree. It was kind of old and overgrown, but it was really, really big. And I thought, my golly, that's going to kill it for sure. But that thing came back better than ever, and it was beautiful for the next number of years. So for pruning to rejuvenate, it's not the time to be timid. We can cut all the way back to four to six inches. What we do that is in late winter, early spring, before things leaf out. You see, if we allow a lilac to totally leaf out and then cut it all the way back, it's wasted a lot of energy. Instead, if we do the rejuvenation pruning all the way back before they leaf out, when the weather warms up, we're going to get a good push of new growth from the roots. They're going to have all that energy that'll produce nice new branches, nice fresh growth, nice new leaves. Now, when you're rejuvenating things like the lilac, remember I mentioned that if you do that pruning of lilacs in the spring, you're going to be cutting off the blooms. Well, yeah, when you rejuvenate a lilac, it's not going to bloom the first year after that, but that's okay. You're going to lose a year of blossoming, but you're going to get a whole new shrub as a result that's going to bloom beautifully for years and years then. Now, some shrubs, though, do bloom on what's called new wood. Even though you cut them all the way back, they'll grow back nicely and they bloom on that fresh wood. That's like the yellow-flowered potentilla that you see or the pink-flowered spirea. They'll bloom on new wood, so they'll bloom the same season. It's interesting, the yellow-flowered potentilla, if we don't do rejuvenation pruning every so often, they really get old and woody, and all the blossoms are up on the top, and they don't look so good anymore. So cutting those back, potentillas, every three to four years really, really helps. Another shrub, you see at the base there, dwarfkrieg and lilac, and also one of the nine barks. So this type of pruning rejuvenation works really, really well every so often when the shrubs look like they're getting old and woody with a lot of old branches inside. I wanted to spend a little bit of time on pruning specifically hydrangeas because they're so popular and they're so beautiful. Now, here we have the Annabelle type hydrangea. The botanical name is hydrangea arborescens. They're the ones with a big white, and there are a couple of light pink varieties now. But the Annabelle hydrangea with the big white clusters, each winter they freeze back to close to ground level, or nearly so. And so the pruning in the late winter, early spring, is all the way back. Or sometimes you'll see in April, early May, they'll start sending out a little bit of growth, a few buds on the twigs. So you can kind of see where that new growth is coming. But as a rule, they can really get pruned back to about six inches above ground level. If you didn't prune, the hot branches all die back pretty much. And the new growth starting at the base has to grow back through all that mess of old wood.  There's another beautiful type of hydrangea that's fully winter hardy. And these are called the penicillata hydrangeas. These are the ones with the pyramid or panicle shaped flower clusters. Aren't those beautiful? One of the very nicest ones is called vanilla strawberry. There's all kinds of new hybrids of that. Some are pinkish white, some are green, lime green, white. And these grow more like what I would call a normal shrub. Now remember the Annabelle type freezes back all the way to ground level or almost. These leaf out from the upper part like a normal shrub. So the pruning in the spring of the year is mostly just to trim off those old flower clusters. Those flower clusters look kind of neat over winter, so many of us leave them on. So trimming off the old flower clusters and just maybe trimming the shape a little bit is all the pruning that the penicillata type need. You know, you can do a little bit of thinning out of weak branches to encourage better flowering. Evergreen shrubs. Similar to pruning evergreen trees, there's kind of a window of opportunity with evergreens. They can really be pruned really the first half of summer. On the left-hand side we see creeping juniper. Sometimes they need to be kind of trimmed as they encroach on the sidewalk or encroach on other plants. Arborvite are the beautiful columnar shrub on the right-hand side. And also they can be pruned really pruned shaped during the first half of the summer. Next we go to hedges. Now formal hedges are making a comeback. It's kind of neat. Some people will put a little low-growing hedge around a perennial flower bed or to divide property. Hedges are making a comeback. They were very popular in the first half probably of the 1900s. Now here's a fascinating point. There's a right way to trim a hedge. And there's a way that's not quite so good. The right shape is, if you see all the way over on the right-hand side, the right shape is pruning the hedge so that the base is wider than the top. And here's the reason for that. If the base is wider, the branches at the base are going to get sunshine. And that will keep them in good leaf. If we don't, if we just take a hedge and just shear right across the top and maybe square it up, the upper branches tend to shade out the lower branches. And pretty soon the lower branches are bare. They've lost their foliage and then the hedge just doesn't look as good. If you've ever visited the University of Minnesota Landscape Arboretum, they have a hedge collection with, I think, up to 70 different types of plant material trimmed into hedges, you know, solid long hedges. And nearly all of them are all pruned into that shape that you see at the right-hand side where the lower part is wider than the top. It really makes kind of a neat, neat look. Now, rejuvenating a hedge. Well, what if you didn't keep the wider part, the lower part wide and it got all kind of bare at the base? Well, hedges can be rejuvenated too. And sometimes the rabbits will do that for us even, won't they? They'll nibble on the shrub or sometimes they girdle the branches so that all the top is dead and you need to cut back. Well, these deciduous type hedges do rejuvenate very nicely. In the late winter, early spring, as soon as the snow disappears and you can, you can cut them all the way back to four to six inches above ground level and they'll come back nicely. I should mention one thing about rejuvenating shrubs, deciduous type shrubs. By the way, evergreen shrubs, evergreens, arborviety, juniper, they do not rejuvenate. Well, they don't have the capacity to send out new growth once cut back like this. So evergreens just are not that flexible. I wish they were. But there's one other thing I should mention when rejuvenating a hedge or any shrubs, deciduous shrubs, cutting them all the way back works beautifully in 99.9 percent of the time. First of all, these shrubs have to be healthy. They can't have, they can't be too weak because maybe that indicates that there's root problems or something and they don't have the energy down below to burst forth. Or the other thing that I've noticed is if an old shrub, there was maybe planted 30, 40 years ago. If in the meantime, the shade tree, shade trees have also grown for the last 30, 40 years. And maybe a shrub that was once in the sunshine, such as lilac, is now all of a sudden in the shade and not in its preferred sun. And so in cases such as that, if a sun loving shrub is now years later in the shade, it might not have the energy to come back. I haven't seen that very often, but I just always like to mention that, that there's a small percentage of shrubs that won't come back. But if the shrub looks healthy, other, but it's just kind of big and overgrown and old dead wood, it's got fresh wood, then you can go ahead and rejuvenate them. Now I'm excited because we've got a brand new weekly podcast that we started about a month ago. It's a joint effort between Forum Communications and NDSU Extension, Cass County. And it's a gardening podcast called Growing Together. And it's free and open. It's not a subscription type thing. You can access this anywhere you get your podcasts or you can go on the Inforum site and just scroll down and you find all their podcasts. But just even by doing an online search, growing together a gardening podcast, you'll find ways to access that. And so each week, Forum reporter John Lamb and I have a discussion about gardening. One episode we did house plants. We did recently did pruning your tools and taking care of your garden tools. Tomorrow we're going to tape and then it'll probably be next week available. But we're going to talk about the emerald ash borer and what we can do to save our ash trees and the seriousness of it. So anyway, I just wanted to mention these are fun podcasts to produce and I hope you would enjoy listening to them again there. Just if you visit wherever you get podcasts, there's no subscription needed. It's free and open to everyone. And if you ever have any questions, do feel free to email me. And so I'm going to leave that up there for just a minute or so. And then we're going to go through these questions. And if anybody needs to duck out early, I just want to thank you all for joining. I really enjoy our visits here during these webinars. And it looks like we had about over 180 people join this evening. So thank you again. And so again, if anybody needs to sign off, I really appreciate your joining. So let's look at some of the questions here. Someone asked for the email address and it is there. Donald dot Kinsler at NDSU dot edu. Okay, next question.  Okay, well, one good thing about tree diseases is they tend to be specific to certain types of trees. For example, the black rot kanker is on apples, crab apples, flowering crab apples and members of that tree species. There are other similar type rotting kankers that will get in other trees. So they may not have that exact fungus that causes this, but they can get similar type things. Can you talk about pruning oak leaf hydrangea? My question would be, Carrie, where are you from? Actually, oak leaf, I appreciate the question. Oak leaf hydrangea is very borderline in our zone three and four, which encompasses most of North Dakota and Minnesota. Other areas of the country are able to grow oak leaf hydrangea and oak leaf is quite descriptive of the shape. And so can you talk about pruning oak leaf hydrangea? Oak leaf hydrangea would be pruned more like the peniculata type because if my memory serves me correctly, oak leaf hydrangea does not freeze all the way back. So you could kind of trim that a little bit, take out some of the weaker wood, but trim that before they leaf out. So that's interesting. There are several species of hydrangea that are not fully hardy. Oak leaf is not hardy for zones three and four, as I mentioned. And also the endless summer series with the blue and kind of purplish type flowers, those aren't as fully adapted. Excuse me. So next question, how important is it to clear out the soil underneath fruit trees? Can the garden soil carry disease? And excuse me, it's the point of the day where my voice starts getting a little hoarse, so part of the interruption. It's very important to clear out the soil underneath fruit trees because apples, plums, can harbor insects in those fruits. And insects can overwinter in those fruits and exit the fruit and go into the soil. So it's very important that right after fruit drop that we do get those up and off underneath. Great question. Thank you. Okay, next. I have a crab apple tree, not sure it's aged, but at least 25 plus years that only has growth on half the tree. It used to blossom all over about 10 years ago. It seemed as if half of the tree died. Is there any help for it? Well, that brings up the question about how long do apples, crab apples live? The average age is probably between somewhere between 25 to 40 years. Now, that doesn't mean that the tree won't live longer. It's kind of like humans. You know, some humans live to 120 years, but that's kind of the exception. We have certain human average lifespans and apples, crab apples do too. So 25 to 40 years is kind of the lifespan. So your tree that's at least 25 years is getting a bit older. And at that point, sometimes they'll start developing problems. So if half the tree doesn't have growth on and if nothing has grown on that for at least last year, that part is must be dead. You can do the scratch test, you can with your thumbnail scratch the twigs live branches will have right under the outer bark will have a fresh green layer called the cambium layer also bend the twigs if they snap, then that trick twig is dead. So I'm kind of guessing half the tree is probably dead. And there's nothing that will be able to be done. That would would kind of have to be pruned out, which will leave you only about a half a tree. But I'm suspecting that the tree, you know, in 25 to 40 years, they do develop kind of old age type sicknesses. And so I'm afraid there's probably not going to be a whole lot. If you've still got half the tree, it might be a good time to start a new apple tree. Thanks, that's a really good common question as well. Our apple trees are over 20 feet tall enormous out of control the best approach where do we start and how much do we cut. Well the time to do that type of pruning getting an older apple tree kind of down into shape into a height you can manage. And a manageable height is really around 12 feet is the target height for an apple tree. So an older tree. Do the do the trimming over a couple of years, you know, maybe three, four years, and start at the base and make that the widest branch, you might have to tuck that a little too but the end result with that bottom branch would be the widest and then tape your way up, tape your way up as you go. And make sure you do that during the dormant season, because that can be a little bit hard on tree but the reason we don't cut that all the way back in one year is that can be too traumatic on a tree. So we do a little bit each each year. I have a contender peach a contender is one of the more hardy peaches for our area so fun to experiment with contender or reliance a contender peach tree that's in its third winter good by previous pruning years done early spring will dormant have caused a lot of die back. What is the correct time to prune stone fruit. Generally the plums peaches should be well dormant. But as you mentioned you've caused a lot of die back. Instead, especially where peaches are certainly borderline even contender variety. Wait until the buds have started expanding a little bit, and then the growth will, the tree will be active and it will seal over those pruning wounds so try delaying a little bit on that for the pruning. I think that might be a good case for rather than doing it well their dormant kind of doing it as they're starting to come out of the dormancy and having a little growth. Next question isn't actually pruning issue but we have a very young apple tree appears a deer or other animal roughed up the main trunk and exposed. It's a long area on one side of the trees or something we should do to help the tree. If the bark is jagged due to animal injury, take a sharp knife and trim off anything that is ragged. There's a nice clean cut. There's no pruning no pruning sealers or anything that will help it. If, if less than, if only about one third of the bark has been scraped away the remaining two thirds of the circumference. If you follow me you know one third injured, but the remaining two thirds of the trunk is okay. Then they'll oftentimes heal their way out of that. So if half of the trunk all the way around is ruined, then the tree might not survive. Do pairs prune differently than apples? Pairs prune basically the same way as apples. Pairs are very susceptible to fire blight disease so typically they're pruned well dormant when the fire blight wouldn't be active. Does delayed pruning apply to other fruit trees as apples? The black rot is primarily a problem of apples. But I'm kind of thinking again, we're rethinking some of these timings of things. And I'm wondering if some of the other fruit trees as well as like plum trees. I'm wondering if plum trees also should be delayed. We discussed the peach tree. I'm wondering if they should also be delayed a little bit until you see the buds start to open a little bit. An exception is probably the pears. Pairs are so susceptible to fire blight and so maybe leave pears during the dormant season. And but maybe let's examine pruning some of the other fruit trees while some new growth is starting. Okay, I appreciate the advice on apple pruning. Two special challenges. Hat trick apple. Oh, cool. Someone has, William has trained an apple in an, I never know how to pronounce it. Is it espalier, a French word, I suppose it's espalier. On a cable trail is awesome. You train those. So it's all the branches are in one plane as in up against a wall almost. Okay, grafted with three apple species. Cool. All of them aggressive, vertically in response. Advice to maintain the form, keep the fruit buds setting tight. A good detailed question. Would you mind, John, William, would you jot down my email, Donald dot Kinsler at ndsu.edu. If you wouldn't mind emailing your question to me, because espaliered apple trees do have kind of a detailed pruning system. I see you do have your email there. So I'll try to save that. Thank you. Can you rejuvenate snowball bushes, Nikki asks. And yes, well, there are two different things called snowball. Sometimes the viburnums, sometimes the hydrangeas with the big white flowers are sometimes mistakenly called snowball, but the snowball bush that you're probably referring to is the snowball viburnum. And yes, they rejuvenate beautifully because they're kind of, they're kind of notorious for becoming rather woody and kind of old looking. So yes, snowball, get beautiful snowball shaped blossoms snowball viburnum. So yes, rejuvenate that is needed to. I have two overgrown burning bush. They're growing over the sidewalk. Will they benefit from rejuvenate? Yes, burning bush uonymous can be rejuvenated quite nicely during the dormant season just as spring is approaching. When should hydrangea be pruned? I was told that cutting them back in the fall means they won't flower the next year. As we mentioned, the anabelle type hydrangea that always freezes back to near ground level, those bloom on the fresh wood and so pruning way back. But the pruning should be done in the spring and not the fall. And I think we covered hydrangea pruning probably okay, so I hope I answered that earlier. Do you prune shrubs at the same location specifically on the branch as trees when promoting more growth? I have a lot of three year old flame willows. Yes, when pruning shrubs back, you would prune them back to where there's a side, either side bud or side shoot. So also to avoid any dead stubs. Regarding hydrangeas, doesn't new growth come from old growth? Well, it depends the type of hydrangeas. The anabelle type hydrangeas, all the blossoms come from new growth. And so that's why you cut them all the way back. They send out beautiful new growth and they bloom from that new growth. So, but other types of hydrangeas bloom from what's called old growth. And that's why with the peniculata types, we don't just cut them way back. We just do a little bit of trimming so it maintains old growth, plus the new growth that will come. So, so yeah, regarding your question on hydrangeas depends on the type of hydrangea on that. Okay, next question from Cindy. How do you determine what branch to cut back and how far if you have two leaders? A tree I just planted last year has that problem. Both leads are the same height. It's important on many trees, both apple trees and shade trees to have one central leader, rather than a Y or a V, because that's a point which maybe 20, 30 years down that tree can split apart at that weak point. So it's important to let one of those become the dominant leader. If they're both the same, well then just take, you know, if one's maybe a little sideways to the other, cut that one back maybe by half to make sure that the one leader is highest. That has what's called apical dominance in botany. And that's the one that will continue growth. So nip the other one back maybe by half if you have to, so that one becomes dominant. Can you talk about pruning roses? I'll save that for maybe towards the end. I do a whole program on roses. Well, basically, let me cover it quickly. Roses love to be pruned. The more the better. The timing is in early spring, late winter, and they prune flower beautifully on fresh new growth. So prune them back by half or so, and thin out a lot of the weak branches so that you're left with some of the main predominant healthy canes. So I hope that'll give a quick quick snapshot on pruning roses. Anything different or unique in pruning a pear tree versus apple tree, shape them about the same as an apple tree. What type of tree would you recommend for a backyard? A year ago, we had to take out a huge boxelder. Boxelder are a good tree, fast growing, but they're short lived. And so a good replacement. Check out lindens. There's quite a number of very beautiful lindens. Japanese tree lilac. It's not like a shrub type lilac, but a Japanese tree lilac is a beautiful one. Also, Ohio buckeye. Do an online search for NDSU variety of Ohio buckeye. Beautiful trees. If rabbits do some pruning on a fruit bush, should they be cut back further to prevent disease? Okay, if the rabbits didn't do pruning back to a bud or a side shoot, yeah, then absolutely. If the rabbits weren't judicious in their pruning, then sometimes rabbits will just nibble a twig and they don't care where they prune. So they leave dead stubs. And so, yeah, take a look where the rabbit did their pruning and make sure that you do prune back to a side bud or a side shoot. Oh, and Kerry mentioned you're in Missouri. Sure, that makes sense on the oak leaf hydrangea. And so I hope I answered that. Okay, yeah, so you're you're in a zone in which some of the other species of hydrangeas can grow. And but I hope that helps oak leaf hydrangea blooms on old what's called old wood so we don't totally cut them back or you'd lose the blossom for that year. So a little bit of judicious pruning on those without a dramatic cutback. What concerns you have pruning American Elm trees pruning American Elms. Elms are pruned in the wintertime the dormant time, when the Elm bark beetle would not be active. So that would be the main concern is not to prune American Elms during the active growing season. Insects have been shown to be able to smell things smell. They seem to smell somehow or detect pruning. And so a freshly pruned American Elm during the growing season when those beetles are active. Beetles would probably be able to sense that and come and invade that if an elm tree is dormant it's not sending out the same whatever they send out. Tara says I'm in southern Colorado but doesn't most of your information apply. Yes, absolutely. The information that I provided pretty much is applicable applicable to most time zones or winter hardiness zones I should say if I've done rejuvenation cutback in the fall is there any special fertilizing I should do in the spring to help them along spirea and shrub roses. Well, the reason for prune for fertilizing those in the spring is because they both bloom nicely and they're heavy feeders. So yes prune fertilizer spirea and shrub roses in early May. That will help them to bloom really really nice and put out nice new growth. At what point would you suggest pruning a one year old hibiscus these shrubs are at our Florida home. I am from the north and just learning the zone for Florida and of course hibiscus here in the north country we can bring those in indoors in the winter and make them think they're in Florida and then back out again in the summertime. So pruning hibiscus we would prune them outdoors kind of like what we prune indoors and that is during kind of the season in which they're resting. Kind of in the wintertime in Florida when they're resting and not blooming then just kind of shear the trim not shear but selectively cut back some of the branches they'll bloom better on fresh growth. So pruning back stimulates some fresh growth. So, so I hope that helps somewhat. How do you make birch trees grow in this area of the country. Ah, birch trees, birch trees like cool moist and of course our summers can be kind of hot and dry. So the first thing is to put a birch tree in the proper location somewhere where it's maybe got a little bit of a micro climate in the yard that's going to stay a little cooler. So not in the middle of a planting bed that's mulched with rock rock gets so hot. So mulch them with wood product shredded bark mulch them with that to keep the soil nice and cool and more moist and make sure that you soak them well so that they never become drought stressed drought stress is really devastating to birch trees. And so birch can grow well if the soils kept cool and they have really plentiful moisture. I have a lilac tree that's four years old the deer got to it pretty badly the second year doesn't have much if any new growth should I still give it time a lilac tree. Now I'm thinking that's probably the dwarf Korean purple blooming lilac that's grafted on to a little trunk. My wife Mary and I have those two they're pretty so a lilac tree. Now I mentioned Japanese tree lilac that's a total different that's like a more of a shade type tree or or decorative tree lilac tree are like grafted where you graft the dwarf Korean shrub kind of on to a trunk and the deer got to it pretty badly the second year doesn't have much for any new growth. I'd give it time to see if it will develop because sometimes they will come back from injury like that. So give it a little bit of time but if the deer totally ruined it sometimes we do need to know when to let go. How would you prune a Juliet cherry bush Juliet is one of the nicer hearty. Cherry type large bush small tree. So how would you prune those would be pruned during the dormant season or just as they're starting to come out of dormancy and depends on whether it's been grown as a shrub type or a tree type more single trunk oftentimes are multi trunk. And so the main pruning of that would be to keep it within balance so it doesn't get so terribly large and out of out of balance so mostly height pruning on those and then thin out the branches a little bit too. I hope I'm not going to some of these could be programs entirely by themselves so I'm hoping I'm not being too brief on some of these. Do you know of any tree phone apps that identify plant shrubs trees. Well, there are some wonderful new plant apps that will identify trees. I may not be able to pull out of my head. The one that's shown to be most most accurate always feel free to send me a photo to email me a photo. I'm not coming forth with the with the I haven't experimented too much with the phone apps, but there are a couple that are kind of cool so that's on my bucket list to kind of find out more about those so not much help to you on that. Yeah, if somebody if somebody is still listening and think of of their favorite phone app hopefully it would jog my memory. How and when do you thin raspberry plants raspberry plants need pruning because most raspberry varieties bloom that will be the canes grow one year. They survive winter and then they produce fruit on those canes the second year and then that came dies. So in the late winter early spring in a raspberry patch you identify the old brown canes and those are the ones that fruit last year and they're dead and you can kind of see they've got just their old woody brown colored bark and those you would just cut off at ground level. The fresh canes and you'll be able to tell the difference when you're in there those are the ones that will produce fruit this year. And during this growing season you'll get new canes coming up from that so key point there is if they're old the old woody. Identifiable raspberry canes those are the ones that you would cut out as as spring approaches we have an apple tree that looks like a bush is a reason that it looks like that could be that at one point it froze back. Or maybe a deer or something nibbled it all the way back and ruin that central leader. So it's interesting if it's still if it is still if it's fruiting I guess you're okay but generally the favored. The favored shape is a single leader with branches off. So I guess it would depend whether or not it's fruiting as to what to do but kind of instinct instinct tells me that maybe you'd want to try to investigate and see if there's still a structure in there that could be less bush and more tree like black growth on a Canadian red cherry tree. Excuse me. Canada red cherry another name for that is the Schubert joked cherry it's the purple leaf ornamental tree and that has a very serious disease fungal disease called black not not to be confused with the black rot of apples but black not on Canada red cherry is also fungus disease. And when you need when you prune out it looks like coal on a stick. It has a very distinctive shape quite gross kind of cancer is looking coal on a stick and that needs to be pruned out and you need to prune back at least 12 inches below where you see that that narrow cancer is like growth and should be cut off during the dormant season. Any advice for okay raspberry bushes spruce and evergreen trees with shedding needle disease also known as needle cast disease. And cutting lower branches off of an older tree. Well any any spruce tree branches that are dead should be pruned back all the way to the trunk if there's no needles on if it's determined that they're dead then cut all the way off back to the main trunk. And any ideas to stop or slowing down this disease. It's called needle cast needle cast disease of spruce it's a fungal type disease and it causes the needles to become very sparse and it can kill trees it can kill the lower branches. So do an online search for needle cast disease NDSU and that will tell you the timing of a fungicide it's the fungicide active ingredient is called chlorothalonil it's the most common fungicide so if you look for a fungicide for trees and shrubs or an all purpose fungicide it'll have chlorothalonil in it most likely. And the timing of that is about mid May to protect the trees. So again do an online search needle cast disease NDSU and you should find it right up. Can why Gila be rejuvenated cut absolutely why Gila are beautiful kind of a pinkish red or purple flowering and why Gila get kind of old and woody after a while without a lot of bloom anymore. So why Gila can be rejuvenated as well down to about four to six inches. The best way to prune gooseberry and red current bushes we relocated a few last year should wait to prune the relocated. If you didn't move them that can cause a lot of root loss naturally when you dig them up so I would prune them back. If you can stand it maybe about a half even to compensate for probably half of the root that was lost. So I would I'd prune them back by at least a half before they leave out this year. Okay. Okay, thank you very much Terry. My end the summer hydrangea survived at least 15 North Dakota winters but as time goes on has very few bleem blooms and this summer hydrangea is a species more closely related to the florist type hydrangea and so it isn't quite as well adapted. They're sold a lot in the in the garden center trade more so in the national chain stores. So a very few blooms I would prune it fairly heavily your end of summer hydrangea but a key point there is make sure that it's growing in a shredded bark mulch to keep it cool. Make sure it's getting lots of water and fertilize it maybe with a bloom type fertilizer water soluble type plant identifier app plant identifier app. So is that the name of the app. I'm going to have to do a little more research on those because I'm so curious to with those apps to aim them at some of the plants that we know what they are and see some of these apps are really really good. Approximately how long does it take for quaking aspen to spread and get newly sprouted branches. Should those be cut or allowed to grow when they come up quaking aspen grows in tends to grow naturally as kind of a multi stemmed tree. So they can be grown single trunk but in nature they oftentimes have more than one kind of a half shrub half tree, you know, big shrub shrubby type tree. And so you can let all of those sprouts that come up you can let those grow it's kind of natural. Again it's personal preference as to whether you want to prune it to single trunk or let it go multi trunk. The natural shape is kind of multi trunk for screening quaking aspen are very very good so maintaining some of those lower branches arising from the base does help in screening. Good time to cut back Carl Forrester grass Carl Forrester is the most common ornamental grass grown in our area, and the time to cut that back is in early spring before any growth starts to get rid of that old and it can be cut down right down right above ground level and the new grass is going to come from kind of the base lower crown area between the, you know, right above the roots, and that can push so much better through, you know, if you don't have all that old growth. Picture this app thank you Tracy picture this that is the one those I was trying to pull out of my head picture this app is a wonderful plant app thank you Tracy appreciate it. Let's see that's all in the Q&A. Thank you 85 of you for hanging on any advice on fig trees. Now fig trees, the best I can do on fig trees is the indoor weeping fig, which respond quite nice. One of the fun things about these webinars is people from all over can join in. And I'm not going to help much on fig trees because other than the weeping indoor fig I've never grown a real live fig tree. You know I have a bucket list a mile wide that would be fun to do a plant a fig tree and see if we could get it to over winter outdoors. So I'm Franco I'm going to be probably not much help on the fig tree. Thank you let me just do when is the time to prune peach trees and doesn't take hard pruning a peach trees. But again, we as we discussed to avoid die back maybe wait until branches are starting to leaf out a little. Is there a way to remove one tree or shrub that is grown up with another. Good idea. Good question a sumac growing up within a spy area.  Or another thing is if a seedling tree seedling a seed falls in and you got a an elm tree growing in the middle of your spy area. The best way to eliminate those if you can't dig them which often becomes almost impossible. You could try with pruning loppers or shears to cut down as far in if you can get down into the root enough and cut that out that will work. There's one other method that's a little more risky. But if you cut the offending tree that's growing in the middle of something else, if you cut it all the way down flush with the ground and then very carefully with lawn weed killer in a detergent bottle or an eye dropper. Precisely put lawn weed killer on that cut surface that you want to kill and do it immediately so it can absorb it. But again, that needs to be with precision if that lawn weed killer got onto your spy area, it would damage the spy area. But we did do that a fair amount when I was a young student in the horticulture plots. When there was an offending tree growing in the middle of another shrub, we would cut it all the way down, squirt that cut surface, and then put a little handful of soil over the top so the fumes wouldn't affect. Let's see, I think we're about to the end. Two young locus trees. The tops died last winter is okay to prune the tops off. Yes. What caused that sort of loss?  They're usually pretty winter hardy, but almost anything can freeze back.  Hopefully they would send out a new leader to take off. So it sounds like probably a winter type injury. Good. I think I think I think I covered everything. Well, again, thank you. 77 of you held on right to the bitter end. So thanks again. I really enjoy these webinars and thank you much. And I do like to keep these live and interactive. We will have a recordings of these that we will send out to all those that registered at the end of the webinar series. So next week, Wednesday evening, 7pm is the webinar on getting everything ready for spring. So thanks again. Thanks again. Thanks for enjoying joining us and I hope you enjoyed the evening as much as I did. Thank you very much.


Alors oui, je voudrais remercier les organisateurs de cette éventue pour la possibilité de parler ici. J'espère que je vais avoir des choses intéressantes pour vous. Et donc, let's start. Et le titre des différentes lectures est, le titre global est hyperbolicité et généralisation. Et j'aimerais commencer par des exemples de plus en plus. Et l'exemple de plus en plus que j'ai dans la main, c'est le point carré space-model pour le plane hyperbolic. C'est très simple, c'est juste de déclarer que l'H2, le plane hyperbolic pour ce modèle, est le plane à l'extérieur et avec des métriques. Donc, à ce point, x plus iy, on met cette forme quadratique sur le plane tendant, on va dire ça. C'est-à-dire que si j'ai un parc, c'est assez régulièrement, sa longueur sera simplement l'intégral sur le domaine, je dois dire sur lequel c'est défini, et sur l'intervalle de, bien, la norme de sa vitesse. Donc, la norme de x'2 plus y'2, sorry, la route square root de x'2 plus y'2, divisé par y of t. Ok, donc, qu'est-ce que ça ressemble à ? Donc, quelques facts en ordre. Donc, la ligne verticale de la géodésique et les circonstances en r, comme ça. Donc, ici c'est r, ici c'est le plane à l'extérieur, et nous avons la ligne géodésique, donc la route de la petite longue entre deux points, qui sont comme ça ou comme ça. Donc, il y a beaucoup. Mais, même deux points, il y a seulement une géodésique entre elles. Et la groupes isométriques de l'orientation de l'orientation de l'H2 est isomorphique à PSL2R, actée par une homographie. La action A, B, C, D, appliquée à Z, sera élevée à AZ plus B, ou à CZ plus D. Et c'est PSL2R, parce que la identité minus est triviale. Donc, c'est exactement le kernel de la action, et c'est pour ça que l'action s'actualise au centre. Ok. En fait, vous avez déjà prouvé ça avant de trouver la géodésique. Et la action est conforme. Pourquoi parlez-vous de ça ? Parce que les objectifs principaux de ces discussions seraient les groupes, les groupes hyperbolicités et les généralisations, qui sont les plus importants. Et l'H2 est un bon espace pour quelques groupes. Donc, qui sont-ils ? Donc, le premier, peut-être le premier et le plus fort, c'est le groupe modular PSL2Z, qui a une bonne fortune, je ne sais pas si c'est une bonne fortune, pour préserver des très bons objectifs dans les planes de l'opportunité. Donc, chaque fois que j'enlève cette ligne horizontale, je veux dire que le plane de l'opportunité est quelque chose d'intéressant. Donc, ici est 0. Ici, c'est le circle de l'unité. Ici, je pense que c'est de l'unité. Et quelque part, ici, ici, c'est l'exponential de l'unité par 3. Et, pour moi, let's draw this arc here and call it A. A will be the geodesic, but for the geodesic for H2 between i and exponential i pi over 3. What happens to A when I apply PSL2Z ? First, I have this matrix, which is 0, 1, minus 1, 0, which flips A over i. And then I have 0, 1, minus 1, 1, which turns A of angle 2 pi over 3 around the other endpoint. And those two matrices generate SL2Z, so PSL2Z as well. So I claim that PSL2Z, A, this is very classical, the orbit of PSL2Z applied to this segment A is a tree, the modular tree, or the serre tree, sometimes I heard that. I believe. It is completely explained and detailed in Serre's book, cours d'arithmétique, non, cours d'arithmétique, which I don't know the title in English, and it's a course in arithmetics, maybe. And that's probably why we call that serre tree. So what do I want to say ? Yeah, I was going to write something PSL2Z of A, the orbit is a tree, meaning this is a connected graph without cycle. Oh yes, it's a modular tree, PSL2Z. It looks like that, let me finish the drawing.  We still have those arcs that continue there, and each time we arrive to a vertex here, it's unfold three times. But of course, here also, because here is the image of I, but below is the image of this point. So there is a three fold here, and so on. So this is the kind of pictures when you start, you don't know when you finish. Ok, maybe I finish now. So it's very interesting to have a space on which a group act, that's what groups are made for, acting on spaces, that's why they are interesting. So here we have an action on a tree. Another group for which H2 is interesting. Yeah, I'll come back a little bit to this picture. Another group for which H2 is interesting is a fundamental group of surfaces of genus, I need a base point, of genus G, closed orientable surface of genus G larger than 2. So it looks like that, for genus 3 for instance. So what happens here? I claim that H2 is a good model for universal cover of sigma G. There are several ways to see that. One, for instance, is through uniformisation, Riemann uniformisation theorem. But I'd like to just mention more down to earth way, maybe. Ok, let's do that for sigma 2, or let's sketchly do that for sigma 2. How do I get sigma 2? Sigma 2 is very simple. It looks like 2 torrées glued along a common boundary and indeed it is. So it comes from 2 torrées, so rectangles, but with a boundary, so pentagons with sides glued like that. So if you ever glued the sides of a rectangle to get a torrées, it would be without trouble seeing that this is a torrées with one hole and the same on the other side, maybe with colour. Ok, so the colours mean something. I'm not identifying this to that. Green arrow is identified, so I should do that. So now if I want to understand the universal cover of sigma 2, well it will be tiled by those hexagons. So, octogons. Sigma 2 is tiled by octogons, or by the way some people manage to draw where the sides go in this picture. I can try, but... Ok, you can try. This somewhere. How is it tiled by octogons on the vertex that is the image of all the vertices of my folded octogons? Around it I see eight different octogons. So with valence 8, meaning that at each vertex there are eight octogons. But fortunately H2 comes to tell us how it looks like. In H2, there exists one regular octogon such that the angles at vertices are 2 pi over 8 so that I can put 8 of them around the vertex. So I know this is pi over 4. So how hard to see that? Maybe I just want to show you where it is. So I'm just drawing H2. I'm choosing I and I'm choosing 8 4 in rays, geodesics, 8 rays, 4 geodesics the right regular angle here. So how it looks like? 1, 2, 3, and I did the fourth one. So it's like a spider, I don't know. And I told you angles make sense because the action of PSL2 is by conformal transformation, so preserving angles. And I want to try some regular octogons. So I travel the same length on each of the rays, the same hyperbolic length and I join them by geodesics. So I don't know how they look like. Ah, come on. Something like that. That's a geodesic hyperbolic octogon if I'm not mistaken. And then I'm trying to see what's going on on the angles here. Well, let's call that this parameter T. If T goes to infinity and you see like very close to an ideal octogon angle is then very close to zero. If T is close to zero you see something that lives in the tangent space essentially. So angles are cloned to the Euclidean situation and you can check that in the Euclidean situation angles of octogons are I don't know how they are but larger than 2 pi over 8. So in between there is somewhere there is a good octogon. So I can take this octogon as a model and build the tiling so that I have a tiling of the Euclidean of the hyperbolic plane actually with the right number of octogons around each vertex. Now I have to check that the action of pi1 of sigma g matches this tiling so there is a little exercise of label checking and it's not very complicated. So the end of this so hence so there is a little bit of checking here but h2 can be endowed with an isometric action of pi1 of sigma g2 that is free and with compact sigma2 that is universal covering action. Ok. So here in these two examples we have two nice examples of actions so psl2z acts on the modular tree pi1 of sigma g acts on h2 should have been more careful. Both actions are by isometries properly discontinuous and co-compact. I just say what means properly discontinuous and co-compact so properly discontinuous means that if I take a compact subset of either of the spaces and I look at the elements I should write it so I write it there so properly discontinuous so for all k compact the set of elements g and g such that gk inter k is non-dempty is finite. co-compact means there exists a compact that meets every orbit or you can cover your space with a single compact. Ok. This is the best possible situation by isometries the one that tells you the most about the group so let me just state define and state what is needed for Schwartz-Mille nor Lemma so I need the concept of quasi-isometries so let me define that if x and y are metric spaces a map from x to y is a lambda mu quasi-isometries so here I should say lambda is greater than 1 mu is greater than 0 so if two things really for all x for all x prime in x for the distance of f of x to f of x prime is controlled both ways by lambda distance of x x prime plus mu and 1 over lambda distance of x x prime minus mu so it's like bilips sheets but with error and there is a second condition which I was not careful enough to put on the same board but that will go just below that it is almost surjective every point is at mu distance at most mu from the image of f ok so I write indistinctly the distance in x and y as d if you prefer I should have put d y here d x there d x there I hope d y there but it makes notations heavier ok and shorts mu normal amount say that if x1 and x2 are proper length spaces and if g act on both properly discontinuously and go compactly then they are quasi-asométrique proper means closed balls are compact and length length spaces means the distance corresponds to infimal length of or minimal length of pass between points sorry oh yes I forgot to say that by isometrics oh and moreover and g is finitely generated that's the consequence of the lemma here I just give an idea of how it works so idea cover x1 by translates of a compact k1 build adjacency graph of a thickening of this cover and show that it is quasi-asométrique to some calligraph g so calligraph of g will be vertices are elements of g are of the form v g gs for s in some generating set which is which is well the the generating set corresponding to the link of k1 somewhere k1 and you have its translate and its link is the set of those that whose image intersect it and after that well it's only about x1 isn't it but there is an eddy part it's showing that given two generating sets both calligraph are quasi-asométrique ok so that's why we are we prefer actions that are property discontinues and co-compact basically because they are more or less all the same and they talk the most about the group in some sense now so I started with early examples of hyperbolicity now I should go to Gromov hyperbolicity which is an adaptation in the core setting of the world of quasi-asométries or of the nice geometry of H2 that we met so a definition so let me give the thin triangle definition of hyperbolicity so a geodesic space matrix x is delta hyperbolic if for all A, B, C, X and for all geodesics the triangle is thin so meaning that the side A, B for instance remains at distance less than delta from the union of two others so B, C union C, A and I'm sure a lot of you have seen this picture before so it means that A, B and C are like that so if I draw the geodesic first I should draw AC and C, B then it tells me that AB must remain at close distance from the two first so here delta is a number of course it is interesting for large triangles much larger than delta and it's there is no cost of thinking of delta as small by the way there are a lot of argument that goes through renormalization makes it gives a real sense of thinking of delta as small even sometimes I was going to 0 so there is nothing special about AB of course this definition is about any triangle so you can replace the rule of points so to illustrate it I started drawing AC and B and C, B but it's really symmetrical this quantity is interesting the distance from C to the branching point ok this is this can be defined as the Gromov product of A and B seen from C and it's formally one half of the distance of CA plus the distance of CB minus the distance of AB so this formula makes sense in any metric space but it's particularly interesting here because we see that there is from CA and from CB and I think of it as like a tripod I'm counting this distance plus this one plus this distance plus this one and I'm removing this one plus this one I'm left with this distance ok so a theorem due to Gromov there is something that I'm missing here how should I operate just the metro full pousse form et pas trop fort ensuite comment je fais pour le récupérer ok c'est ça merci so a theorem is that this notion of hyperbolicity is invariant under quasi isometry if two geodesic spaces are quasi isometric so x1 x2 and x1 is Gromov hyperbolic so it's x2 it's not with the same concern though but we don't really care about the constant the value of the constant so let me define the Gromov boundary of a hyperbolic space so in two steps first I need to define what it means for a sequence to go to infinity or in three steps actually a sequence so let a hyperbolic space a sequence xn goes to infinity if xn xk from x0 goes to infinity with n and k so here I have x0 I have a sequence of points I want that for large n and k they may be far away from each other but mostly their geodesic is far away from x0 and xn is equivalent to yn if the same thing if the Gromov product of xn and yk from x0 or from any point actually goes to infinity with n and k so with that we can say that the boundary of x is the set of equivalence classes of sequences and with the topology with the topology so it is a set of equivalence classes of sequences going to infinity with the topology that comes from the Gromov product so one can extend the Gromov product so this kind of sequences if two sequences go to infinity it makes sense of extending the Gromov product of one sequence with the other and so a sequence of sequences will converge to a point at infinity if this sequence of Gromov products goes to infinity so I hope it's enough to state it like that but the main observation is that so yeah, examples examples if t is a tree it is zero hyperbolic and it's boundary it's totally disconnected if it's a local agipinite tree then it's boundary oh yeah I shouldn't say that it's a tree of SL2Z if it is for the modular tree it's boundary so the modular tree was essentially the regular trivalent tree or also called binary tree non unrooted binary tree so it's a counter set but for H2 it's a boundary of H2 oh, H2 is hyperbolic I think it's an exercise c'est un exercice the boundary of H2 will be the circle at infinity and you can identify it with R union infinity the upper half place model but with the topology of one point compactification here there is an important statement that goes with the setting over there that says what happens if two space are quasi isometric at the level of their boundaries proposition also due to Gromov at this stage everything is Gromov theory so if X is hyperbolic and proper then its boundary is compact and if Y is proper as well and if we have a quasi isometry from X to Y can you remind what proper it is closed balls are compact and if X is a quasi isometry then it induces a homeomorphism between boundary so I did not yet define X is hyperbolic group but let's do that and finish with a tentative application of a nice situation this one definition G is word hyperbolic group this is also definition due to Gromov as most of you probably know the word hyperbolic group if let me state it like that if G acts properly discontinuously co-compactly on a proper hyperbolic length space or for every day's definition it's enough to consider its scale graph for a finite generating set is hyperbolic so for instance psl2z pi1 of sigma g for g larger than 2 and I would like to use my 5 or 5 plus minutes 7 7 to sketch an application of that which I like which I like exemple assume you are given two hyperbolic structure on the same surface ok sigma g g means the genus but also g1 I'm sorry about conflict of notations will mean the Riemannian structure and sigma g the same g, the same genus g2 not the same Riemannian structure are two hyperbolic structure on sigma g ok the theorem it means that pi1 of sigma g admits two actions the first action by isometry which I call alpha1 on the universal cover the hyperbolic universal cover and the second one the first comes from taking the universal cover of this structure the second of this structure sending one orbit on the other gives an equivariant quasi isometry and therefore it's really sending the orbit on the orbit so it's equivariant by by choice and therefore it's a quasi isometry because orbit isometric to H2 and it induces a normal morphism of the boundary so boundaries we understand it's just a circle an homeomorphism of the circle cannot be that complicated can it so in particular it has to be almost everywhere differentiable as any homeomorphism of the circle and the theorem I would like to advertise here or advertise I don't know it's as I understand due to Kouzalo but inspired by mostore rigidity so and I think there is a mention in mostore's work so I will write it like that so if G1 is not isometric to G2 so if I really choose two different hyperbolic structures then this homeomorphism is almost everywhere of null derivative and I'm going to sketch a part of it is very simple conceptually but it uses something that is not here but so so assume that deep side the map and the boundary is not absolutely continuous so it means that there exist a subset E in S1 of positive Lebesgue measure such that deep side of E is sent as 0 Lebesgue measure so now I take the orbit of E for the first action I should say alpha 1 I don't know how to write that well the orbit of E is invariant it is sent to the orbit of deep side of E which is a countable union of set of 0 measure so here there is a a statement that the action has some mergodic property that the only invariant subsets of such uniform action are full measure or 0 measure for Lebesgue by Argodisity of course Lebesgue measure is not preserved but it means that E as full measure its image still as 0 measure so from that one can deduce the claim of the theorem that the derivative that F is singular I should have stated like that so F is no it's not F it's deep side so it makes it does not quite prove the theorem really because it says assume that this is not absolutely continuous then we have a singularity of this application and it's not so far from checking that derivative is null almost everywhere actually null everywhere it is defined and there is what about if it's not what about if it is absolutely continuous I should show you that G1 and G2 are actually isometric so since I'm out of time I will not do that but indeed similar arguments show that deep side satisfies some functional equations which makes it a mobius transformation which makes G1 and G2 conjugate by an isometre F2 thank you for this first lecture