And the Benway State Governor-Everett and Father Hyacinth Alia has said that his victory at the repeal cuts was not for him alone, but for Benway as a whole, and it's called on his opponents in the concluded humanitarian elections to support his administration and join hands to build the Benway of their dreams. Governor Alia appreciated the Benway people for their support and confidence given him in his administration and promised not to fail in his resolve to actualize the Benway dream. The court will appeal to resolve all the matters raised by their parents in favor of the room for the Hyacinth Alia and Samodhi and APC. So we want to appreciate the judiciary for still proving to be the hope of a common man and his excellency is very happy with the judiciary. He said the victory is not just his victory but the victory for Benway and he is calling on his opponents to down two for now concerning litigations now they should come back join hands with him for them to build Benway of our dream. In a swift reaction the People's Democratic Party in Benway State reiterates its resolve to exhaustively pursue the legal option to recover the governorship of the state which it believes rightly belongs to the party. We have decided to exhaust the legal option open to us at the courts as you are aware yesterday the Court of Appeal in Abuja dismissed our petition and they upheld the decision of the tribunal which validated the election of Hyacinth Alia as governor of Benway State on the platform of the APC and we are not satisfied with the judgment of the Court of Appeal as we weren't with that of the tribunal and we are in touch with our legal team and most obviously we will be pushing onto the Supreme Court to have them interpret the you know a brief of arguments that our lawyers had presented before the tribunal.


Hi y'all, she was seven. Okay. So Lately I've been getting a lot of guys commenting on my videos and they're mad at me because I'm kind of Putting them down because they don't want to pay for dates anymore.  I have them waiting there pissed off All excited from the whole week of talking on the phone about this date that they were just Waiting for the whole week and don't show up.   Okay, I'll see you. I'll see you another time. Maybe We'll see and then hang up leave them hanging because Obviously, he doesn't understand a woman's time is very very very valuable And if he's not going to even pay for your meal, he doesn't even deserve your company he deserves to sit there by himself looking like a fool and If y'all have never stood up a guy try it, it's very fun because It teaches people lessons, you know First of all, you know, if you have already been told that you're paying for your own meal And you want to get even to go ahead and do that because it will teach them a lesson. It will teach them a lesson.  He's gonna be stood up So You know, it's it's time to it's it's time to show them, you know Your work if you're gonna sit there and Pay for your own meal After they asked you out Whatever comes after that you can't complain about because that first impression Is how the rest of the tone of that relationship if you do get into a relationship is gonna end up You're always gonna be paying for half of everything and if you don't want that type of relationship Don't even go on that first date Just stand up And I suggest that because these guys need to learn they need to learn the value of company, you know They need to learn that, you know sometimes It is nice to pay for a woman's date and not expect anything in return as I saw in the comments Some guy said well, why should I pay for a woman's date and drinks and meal if I'm not guaranteed anything I said because first of all you shouldn't be expecting anything, but they're company You know, if you want a prostitute or a hooker You can go and pay the same amount as it costs to take a woman out on a date and get some sex Don't say it's dating if you're expecting something in return because it's not You're just looking for sex. So go for a hooker She'll tell you everything you want to hear. She won't even expect to get fed and You know, you can save your little money and give it to her and she'll give you what you want in return And it's just no big deal But when you ask a woman out on a date and you expect her to pay Why should she pay when she can order a pizza at home or order Chinese food or take out at home and relax or Go out with her friends and meet a man who can't pay, you know, that doesn't make any sense so a lot of these guys are going to find themselves alone or Especially, you know, when you get past 40 when you get past 40 as a man and you don't have your stuff together and you're still Playing women. It looks pretty pathetic. Actually, it looks like oh my god.  We have a legacy to offer we have the we have the capacity to you know Bring life into the world, you know, we have the capacity to make a home to decorate a home to make a beautiful home To cook to do all this stuff, you know, if we choose to work We have that capacity to to bring more into the household if we choose, but it shouldn't be Expected and it shouldn't be demanded, you know, especially in this day and age Because if if if it is demanded for a woman to work and bring money into the house Then it should be her choice whether to sleep with you whenever you feel like it or not She should be like, you know what?  So You know, I'm bringing money in the household. I have half say I have everything I don't feel like having sex this month or next month or the next month because I'm gonna be too tired because I'm gonna be working a Lot plus coming home taking care of these kids plus clicking. So I'm just not in the mood ever.     So ladies don't even bother with those. Those those are the kind of guys Who I've seen and Die alone because I used to be a mortician y'all and a lot those those type of guys. They're always in the nursing home alone with Bed source nobody came to visit.  They'd be like, oh my god. What did I do?   They weren't ever good to their own kids They weren't good to themselves. And that's where they end up and the sad thing is They won't see it until it's too late just like men They never realized that they've lost something good until it's too too too late and Once once they realize what happened Once they realize what happened That's What they have to live with, you know by themselves. They don't have anybody to take care of them They're being abused in those homes If they can afford to be in a home, you know, sometimes Someone will just you know, uh They'll be in a homeless shelter or something or in the county hospital just to die and nobody will care nobody So y'all y'all men have to remember that and y'all put a woman down We all treat a woman like trash when y'all abandon y'all's kids and stuff like that Y'all are really doing that to y'all selves later on in life Because everybody knows that there's that that old man That's in the back of somebody old lady's house who um Is paid to take care of them or uh, just that old family member That has at least one person. Imagine if you don't have anybody I have nobody. Where are you going to be? Think about that y'all because a lot of men They no one will even You know come to their need when it's when it's time because of how they were been treated by them and Men forgot to be many men forgot to be men. They forgot what it was To be a man.  I have i've seen countless men Die alone found Weeks later decayed Nobody came to their home because didn't You know didn't have anybody And you know no one came to the funeral. Maybe the kids but they weren't into it. They're like, okay. Well, let's get this over with You know or whatever They didn't want to pay for it. So imagine that y'all. I mean imagine that like I mean y'all got to get yourself together because once you realize That you didn't messed up with women And no women will you know, you're not dateable.  You know, either you're gonna die alone or you can be under someone It's just gonna take all your social security check Anyway, I'm just being funny y'all but um If y'all didn't know, yeah, I used to work for the funeral home and I've seen so many crazy Cases like that. So Just let y'all know it's not something to play with Uh, especially after a certain age, it's not something to play with, you know, don't play with women That's the one thing that people should know.   I'll see y'all later. Bye


So for this story that I wrote for Time Magazine, I wanted to go back to school in the year 2012 and see how it has changed. You know, we've been hearing for years, right, that the price of college has become unsustainable, that the student debt load is now greater than the national credit card debt. And you're starting to see with the cuts in public funding to public universities and community colleges, you're starting to see, you know, truly shocking increases in tuition. And at the same time, we've been hearing a lot about these new online courses. Of course, online courses have been around for decades now, but these were new because they were being offered by prestigious universities. They were full courses, they were free, they were open to anyone, and hundreds of thousands of people were taking these classes. So it seemed like a good opportunity to kind of wade into college as we know it in the year 2012 and try to experience it in all of its different formats, or some of its different formats. So I decided to take physics in several different ways. I'd never taken physics before, it was something I was curious about finally taking. So I signed up for what's called a MOOC, which is a massive open online course. This is one of these courses that, you know, tens of thousands of people around the world have been taking for free. And it was offered by a company called Udacity.com, which was started by a few people who worked at Stanford University and have since left to create this startup. And I also dropped into a class at Georgetown University, you see the sort of other end of the spectrum, the most selective elite end of the spectrum. And I also went to a class at the University of the District of Columbia, which until recently was a community college, now is also a university, but it's basically a relatively non-selective local college, which is how about 44% of Americans are now going to college. One of the things that surprised me about this was that the online classes in general were pretty terrible. Most of them, it was just like a camera in room and a guy was lecturing. And so great, he teaches at Princeton. You know, I'm not at Princeton, you know, there's not like bells ringing in the distance and leaves drifting to the ground. So I'm thinking, you're going to give me something more if I'm going to pay attention to you and not check my email because I'm sitting alone in a room. And then I did find this Udacity physics course, which was different. I mean, first of all, the professor was about 12 or he looked 12, he was really 25, and he didn't have tenure and he didn't have a PhD. He had studied physics at MIT, but he just approached it totally differently. Even though he was teaching you physics in much the same way you would get if you were at Princeton, he also stopped every two or three minutes. So they were these short video snippets where he would be entertaining, but not hilarious, but entertaining, clear description of something, and he'd be writing calculations and a very personable guy, and then it would stop and ask you a question. So you really couldn't disengage for very long. It was like being in a class where you could get called on at any moment. The brain actually learns best in short snippets, interrupted, punctuated by questions. So where you have to, your brain has to sort of take what it's learned and manipulate it, maybe make a connection to something you already knew, or maybe solve a problem that you haven't seen before. All of those things help you do something more than memorize the information and help you actually integrate it into your brain. Looking forward, I think there's really at least two ways this could go, right? I mean, on the one hand, I think that these free classes, if there are enough of them that are high quality like the physics one that I described, then you might actually see something really cool, which is maybe we'll put some downward price pressure on some of the middle-tier colleges. I don't think the community colleges or the elite colleges are going to be dramatically affected by this either way. I think those places are not going away and probably for good reason. But the vast middle tier of colleges, you know, schools that you maybe haven't heard of, but kids are paying, you know, like $30,000 a year to go to, you know, it could be that as these free classes start to gain more credibility and maybe even college credits, which some of them are starting to do, people will start to evaluate, you know, am I really getting what I'm paying for? But I actually think what's maybe even more exciting than that is that it might put some upward pressure on the teaching quality that you see at a lot of schools, because professors aren't incentivized to be great teachers. Like, that's not really why they're there. That's not why they were hired. So particularly with some of these mokes, not all of them, the focus has really been on the quality of the learning. And that's exciting because even though it sounds obvious, that's not how our university system has developed. Thank you.


Hello everyone, in this video lecture we are going to discuss with the wave equation for transmission line, myself Dr. Rupali Shalke working as an associate professor in Waltzens Institute of Technology. Learning outcomes, at the end of this session students are able to derive the wave equation for transmission line and also presents its equivalent circuit diagram. A transmission line is a device for transmitting or guiding a energy from one place to another. There are various types of transmission line, few of them are parallel plate transmission line, two wire transmission line or co-excel transmission line. The knowledge of values of the electric circuit parameters associated with the transmission line is necessary for analyzing and designing. So, on a transmission line when voltage and current is present which results in the electric field and magnetic field in a space in around the conductor. The circuit quantities like voltage and current and field quantities like electric field and magnetic field both are present on the transmission line. This gives a two ways to analyze the transmission line. One way is by we can express the wave parameter by voltage and current using the Ohm's law and by applying the Maxwell's equation for the field quantities for expressing the wave parameters. Now, let us see how they are being used for the analysis purpose. Now, starting with the circuit theory parameters like voltage and current, let us consider a transmission line where voltage V is applied and I is the current flowing through it. Now, we will consider a small length of the transmission line as a dx and assuming that the signal is transmitting in a x direction. The according to the Ohm's law by the relation between the V and R, V is equal to IR and I is given by V by R. The voltage for a small distance dx is given by dV by dx which is equal to IR as it is considered as a transmission line we are considering the resistance in terms of impedance. So, if the equation will become dV by dx is equal to I z and the current equation V is equal to IR will become di by dx is equal to V where y is a admittance. Now, consider or differentiate the equation one with respect to x and using the UV rule we get d square V by dx square will be equal to I dz by dx plus z di by dx. As this impedance z is a constant therefore, the value of the dz by dx will be equal to 0, the derivation of the constant is equal to 0 that is why we get this term is then get 0 and only we remain with the z di by dx therefore, this equation will reduce in this format. Now, substituting the value of di by dx from the equation which we have seen in the previous slide which is equal to V y here after substituting it will get you d square V by dx square will be equal to z y into V and as we see that on the both side the voltage term is present that is why we called it as a wave equation for transmission line in the voltage term. Similarly, let us consider the equation to differentiate the equation to with respect to x then it will be d square I by dx square will be equal to V dy by dx plus y dV by dx here also as V is the constant term therefore, its derivations will be equal to 0. dV by dx will be equal to 0 when we substitute in this above equation then the equation will reduce in the following format. Now, from the equation 1 we will substitute the value by of dV by dx in this particular equation which is equal to dV by dx is equal to I z then it will be d square I by dx square will be equal to y sorry z y into I where if you see on both the side LHS and RHS this equation consist of the current terms therefore, we called it as a wave equation for transmission line in terms of current. This is by deriving the wave equation by considering the voltage and current that is a circuit theory. Now, the value of R and y R given by z is equal to R plus j omega L which is called as a series impedance and the y is given by G plus j omega C which is called as a shunt admittance. Now, if we draw the equivalent circuit for this the equivalent circuit of the transmission line will be a series impedance that is z plus the L and R are connected into the series while G and C are connected in a parallel form therefore, it is called as a series impedance and this is called the shunt admittance. If we see here the distribution of these terms z and y is continuously throughout the transmission line that is why this is called as a distributed transmission line. This is a equivalent circuit representing the transmission line. Now, considering the field theory by considering the field theory let us consider a transmission line with the upper and lower surface equivalent as a script. Here we are conducting strip here we are considering the two transmission line whose length is W is the width of the transmission line and L is the length of the transmission line. The wave is propagating in a x direction as shown in the figure for the field theory we will replace the following terms. We will replace epsilon is equal to L in the which is nothing but a induction per unit length which unit is Henry per meter and mu as a C is equal to capacitance per unit length whose value is f by m that is Faraday's per meter and sigma is equal to G which is nothing but a conduction per unit length which whose unit is Mahos per meter. Using in place of the epsilon mu and sigma we will substitute the L, C and G respectively. Now, according to the Maxwell's equation we are derived the wave equation for the conducting media in the electric field which is nothing but a dow square e by dow x square is equal to j omega epsilon sigma plus j omega mu and e bar L that is we will integrate over the length then this will be integrating e dx dl and but integral of e dl is equal to V according to the Faraday's law and substituting the value which we are considering in the previous slide. This equation will become here we will substitute as a V dow square V by dow x square will be equal to j omega L G plus j omega C into integral e dl will be equal to V which is nothing but dow square V x square plus R plus j omega L plus G plus j omega C. This equation will be considered for when R is equal to 0 here we are substituting the value for the if there is a value for the L then this will be R plus j omega L plus G plus j omega C into V which is nothing but a R plus j omega L will be the series impedance and G plus j omega will be the shunt admittance Z and Y. This is nothing but a which will be equal to the gamma square V where gamma is nothing but a propagation constant. Therefore, the gamma value will be under root of Z Y this is a wave equation for transmission line. Now using the wave equation derived from the MPS law which is in a magnetic field terms. This is a wave equation for conducting media in a magnetic field that is h bar. We will integrate this equation over the length then this equation will be integral del square h del x square del dl will be equal to j omega in bracket sigma plus j omega mu integral of h dL we are integrating h dL but integral of h dL is equal to i which is given by the MPS law then we will substitute this values del square i by del x square plus j plus in place of omega we will substitute L in place of sigma we will substitute G in place of mu we will substitute C and integral of h dL will be equal to i. After substitution we will expand by adding the R term to the first term R plus j omega L plus G plus j omega C into i. If we see that on the and R plus j omega L as a Z and G plus j omega C as a Y. If you observe this equation that on the both side there is a current term therefore, this equation we can say as a transmission line equation in terms of current which is also written with the propagation constant. Now pause this video and consider what will be the equivalent circuit diagram if R and G is equal to 0. Since R and G are the lossy component if R and G are equal to 0 then the transmission line is called as a lossless transmission line and its equivalent circuit will be here there will be no value for the the only there will be a conduction and the capacitance factor. These are the references.


It has been a fantastic preseason. We have been out every day. The temperature has not been cooperating. It has been, I think we've had maybe three or four practices when it was above 32, but the girls have been playing hard. They have been mentally so tough with the cold. We're getting more out of practice this year than I think that we ever have. We're efficient. We're, every drill is super competitive so that we're getting the most out of their sprinting and their defensive moves, their offensive mentality, their IQ is being challenged. And we're really trying a very different approach this year which so far has seemed to really help the team in their creativity and their passion for the game. So we're really, really happy about that. I really think that we have always had the skill to be either in the championship or win the championship. Sometimes when you have two good teams match up, it is 100% about the energy and confidence that each team brings to that game. We are very focused on changing our attitudes this year where we are going to fear no games. We are always going to respect our top level opponents but we are going to head into it knowing we should win, knowing we can win and we're going to try to have the energy to show that from the time we walk on the field until the final whistle blows. We have a large senior class that has been working for four years now, robbed of their sophomore season, had a super tiny junior season and now are coming out with a lot of that energy towards winning games because this is their last shot. I mean, they played as freshmen. Some of them started as freshmen and now here we are all of a sudden in a blink of an eye, it's their senior year and I think when you have so many seniors, we're going to really look to them to provide that energy that I'm talking about. If they want it enough, the remainder of the team will want it for them. So getting them from top to bottom, I mean, I think they have 13 or 14 seniors. So that's a lot of that kind of top loaded experience. We should win every second half. We certainly should win every last quarter and we think that positions ourselves in a way that we achieve our goals, which is obviously a map championship.


I'm Laura Scott with Cal OES. This week, during ongoing severe storms, Cal OES continues to work with local, state, and federal leaders to provide the support needed for community response and recovery efforts. Governor Gavin Newsom requested a presidential major disaster declaration to bolster the emergency response recovery efforts in the county of Calaveras, Kern, Los Angeles, Mariposa, Monterey, San Benito, Santa Cruz, Tulare, and Tuolumne. Cal OES continues to coordinate the response and recovery effort, including deployment of the California National Guard and other state personnel to perform life-saving rescue missions, the mobilization of food, water, sandbags, cots, and other commodities to areas in need, and providing equipment and personnel to assist in the fortification of levees, clearing of debris and snow from roadways, medical support at shelters, and staffing support for local assistance centers. Debris removal has begun in the community of Pajaro in Monterey County, where teams of nonprofit volunteer agencies, the state government, and local county are removing flood debris and household hazardous waste from residential areas. In addition, a local assistance center has opened in Watsonville through April 7th from 9 a.m. to 7 p.m. to support Monterey County survivors and businesses suffering disaster-related losses or damages. Cal OES will continue to ensure that impacted communities have the resources they need to recover from recent storm impacts. To see more from us, go to news.caloes.ca.gov and follow us on all of our social media platforms.


All right, so let's begin To begin can you just please state your full name share grass home and president and CEO of the Mining Association of Canada and your age My age 51 you're actually you're you're one of the young ones So don't worry about it And where were you born born in Montreal? Yeah, and what did your parents do? Well my mom when I was growing up was at home With my brother and me and my dad worked for bel canada Okay, and what did you do as a child? What was your interest remain interest well, I wasn't very sporty though. I didn't ski and swim But I was What I do I like to travel still like to travel like biking I went on bike trips when I was a teenager I Always sort of been a reader Always a bit bookish good at school. What were your Best subjects in school or favorites on this my favorite subjects were always political science history economics those the social sciences Were always my strength, so I came to mining Not not not the normal through like geology or engineering No, that's right, so what was your what was going to be your idea going forward after high school? Did you know kind of what you wanted to do in life or? No, in fact Be honest my career has been It just kind of happened You know I I mean at one point I thought because of my interest in local science. I might go on and study law But then when the time came and I was in university and I finished my undergraduate I didn't really feel like going to law school, so I did a masters And in policy in policy as well. Yeah, my undergraduate was in political science and economics at McGill and then I went and did a masters as well and You know after I graduated I Put with my masters. I knew I had to get a job somewhere and figured Coming to Ottawa might be not a bad idea. It was actually in the middle of a Pretty significant recession in Canada And Montreal was especially hard hit double-digit unemployment youth and youth unemployment really high So I came to Ottawa thinking maybe I could get something and ended up starting my career working for a member of Parliament and then from there it just sort of you know one job led to another job which led to another and If you'd asked me when I Graduated if I thought I'd work in the mining industry. I'd have looked at you funny And I would never have predicted this career path for me but It happened and I loved it and I Certainly never regretted it. So how did you fall into them? I guess what was your first official job you consider to be in the mining sector? Well, how did you start that? Well, the closest I came Was working on Parliament Hill for the minister then minister of natural resources and McClellan McClellan under the government of Jean Cretien and and At the time I Like like a lot of things. I would had a colleague in her office Dan Piskowski and he was her director of Policy for mining and forestry He had the right background. He had a masters in mineral economics and after the 97 election he got a job with Mac and I stayed on with Anne McClellan after the 97 election when she became minister of justice But after about two years Dan Called me and said look there's a job here at Mac Vice president public affairs and communications. Why don't you apply? So I thought well Okay, why not? Didn't knew I didn't know much about mining but also knew they weren't looking For that expertise per se they were looking someone with more of a an understanding of how government works How to work with media and how to communicate and I had those skills so I applied and they hired me and Then I discovered an industry that I found absolutely Fascinating with great people in it really committed to what they do and a sector that With people who Are far from you know some of the stereotypes you might think of when you think of mine and I've Consequently, I'm you know, what is it now? 17 years later. I'm still here Yeah, still in the second. So you started Vice president Yeah, I was vice president public affairs of communications for Mac Started in 1999 worked till 2008 when I got a When I was hired to be the president and CEO of the mining Association British Columbia So my family and I moved out west to Vancouver Yeah, I had three wonderful years best place. I've lived. Oh, yeah, no offense to Montreal second best place more Ottawa third or the And yeah, I just had a wonderful time what I really liked about Working there especially was the industry was all around me on House Street and around so Yes, it was great to sort of be Next door to everybody and really felt your had your finger on the pulse of the sector but after three years my former boss at Mac retired and They came calling and said would you come back and I wasn't sure I wanted to I was enjoying Vancouver so much for those reasons I just gave you and but ultimately decided yeah, I suppose I I should and And came back to head up the National Association In 2011 and I've been here ever since now The president could you explain what basically what the role of Mac is the mining Association of Canada? So we're the national voice of the mining industry Canada's mining industry We represent companies That operate mines from coast to coast to coast wide range of commodities including everything from base and precious metals to uranium to oil and oil fans diamonds iron ore and And we're the the voice of the mining sector as opposed to the PDAC Which represents the exploration community? We really focus on mining And our primary role is to interface with the federal government on public policy so any Rules laws regulations policies that affect mining we would be the the advocate for Mining's perspective on those issues So that's our primary function. It's been what we've been doing since 1935 When we were first founded The role of federal government has expanded its role in mining has expanded considerably over the years Much more so today than when it was first Mac was first created So there's a lot more for us to do Our mandate has evolved in recent years to include Being the voice for Canadian mining abroad to a degree Ours is a very outward looking sector. It's probably the only Sector of the Canadian economy where you can say that we're a global leader not sort of a branch plant of some foreign multinational So Canadian mining is a known commodity in the rest of the world Second largest outward investor to the banks and Really a uniquely Canadian success story So we've become increasingly though the voice of that leadership Outside Canada Just in the last number of years And is because mining has become so global so international This is this M a suit is Mac see itself often Other governments or it's still strictly with the Canadian federal government. Yeah We'll only deal directly with the federal government per se, but other governments often come to us to learn about what it is that we do Particularly in our role around sustainable development and the work that we've done to develop towards sustainable mining That generates quite a bit of interest From other parts of the world, but we'll be involved as well in promoting Canada's trade ties with other countries particularly countries where there's a strong mining Interest parts lots of Latin America parts of Africa Southeast Asia We are strong supporters of free trade and also You know have a strong interest in in ensuring our investments are protected and safe So foreign investment protection agreements another instrument that the federal government negotiates with other countries are important to us So the investments because mines are Very capital-intensive. You're putting a lot of people's money At at risk and so you want to try to Minimize that risk if you can From you know on unfair government action is it does Mac have a Difficult position in the sense that it's often I feel like it's Running after the government to be heard or does the government really understand the role of Mac To get to I guess the the rest of the industry. Oh Yeah, no, I think we're definitely recognized as the national voice The government in many ways relies on us For our views on on issues and we'll come to us ways it it is in fact, you know, there's a couple of times We mean one of the sub sectors of mining that we don't represent and haven't ever represented is thermal coal So there's a coal association in Canada based in Calgary and so we we actually don't get involved in matters that affect thermal coal There's power generation or or other Types of issues that that just our interests don't have and our members don't have an interest in and so when those things come up I know that the government of Canada can find it quite challenging because They want to come to us and And we can't help them And so they've had to end the coal association itself is very small and Have doesn't really have the kind of public policy depth that that we bring to the table Okay Now since we've worked in this industry, have you any role or project that you've worked on that Believe was quite dysfunctional Didn't run the way it should have If there is one Yeah, you know I really think of I'd have to go way way back to when I first started at Mac We had well we still have well There was a program originally called keep mining in Canada then morphed into mining works for Canada and There are elements of that program still alive and well today We would organize we've been organizing a national at an annual lobby day called mining day on the hill every November and Representatives from our board of directors and and other company reps come to town and they meet with officials and politicians political staff Other stakeholders over the course of a day. They can have 60 70 meetings Speaking about issues that matter to the mining industry So we've been doing that. We were the first group actually in Ottawa to organize such an event now Everybody does them these annual lobby days as they're called But we were the first and It was a key part of the program called mining works for Canada and when I first joined the association What I found was that mining works was Very unfocused It was quite superficial. It was promoting Sort of mining at a very high level But without giving what government actually needs which is real information on the issues and our perspective on the issues And so we weren't really getting much traction with people It was we've been doing it for you know approaching 10 years and it had run out of value We felt to to arise that was certainly my assessment and It was starting to also do other in engage in other activities that were also in my assessment of limited value different types of Events in across the country, but that weren't really Targeted no sense of a targeted audience. They were just sort of feel good activities It cost a lot of money, but didn't actually do much and so Certainly for the first few years part of my Challenge was to turn that around and and focus it and reshape it and of course whenever you try to do something like that That's been around for a while There are people who are attached to that model And it can be a bit of a struggle but ultimately we did succeed and and I know I at the time the board itself wanted that change So they were looking to the association to turn it around and I think one of the reasons I was hired as they hope that I had those skills to do that So I knew I had the board support and my president support to do that But there were still people that you had to work with to convince them that was the way to go so I would say it was nearly days frustrating and dysfunctional because we were trying to obviously play a Accomplish a critical objective which was to Advance the interests of the mining industry in Canada with key decision makers and we weren't doing it very well and we need to improve how we did it and It was frustrating to see Where we were at, but then also very rewarding when we were able to turn it around And now is since becoming president and CEO of Mac Have there been any major projects or initiatives or changes that would be worth mentioning? Well One of my other major assignments when I first joined Mac was to develop what became towards sustainable mining or TSM Which is sort of another central sort of pillar now of What we do so when we You know we described earlier what's our function the voice of mining the interface with the federal government But there's another key aspect today which is to Actively work with our members to promote sustainability and mining And we've developed this program that is one of a kind There isn't another country in the world except now for Finland That has a program like this and I mentioned Finland because just last November the finish mining Association Decided to adopt Mac's towards sustainable mining initiative. And so now it's in place in a second country and That decision has also triggered the interest of a lot of other countries and we're now sort of getting deluged with requests from different chambers of minds and different governments around the world wanting to know what is it that we've designed and Implemented here and wondering what's involved in doing the same So that's been something that's Really exciting to watch to watch something that I was involved in very early on in setting up and then see it grow and actually then go global and Continue to sort of spread it's It's certainly a well-respected program and As I said it there isn't another There isn't anything quite like it anywhere else. It's got You know, there's public accountability for performance third-party assurance. We have a national advisory Panel of stakeholders that what it keeps our feet to the fire and challenges us Yeah, it's it's a it's a I think a pretty unique way of engaging with civil society that the mining industry and other countries haven't quite Done to the extent we have but something we're certainly proud of And is it like what are the outlines of the program? Is it things that you? You you kind of have to implement towards the the industry so these are so how it so how it works is every member of Mac every year at the mine site level Or at the level of or smelter or refinery because we also represent smelting and refining They will evaluate their performance against a suite of 23 indicators that cover issues like Greenhouse gas management and energy tailings management biodiversity conservation External engagements Aboriginal engagement those sorts of issues they'll measure themselves against criteria and Give themselves a rating every year that's publicly reported in every third year Those mine sites undergo an external evaluation of their performance and those results are published and then the national advisory panel every year will choose a couple of companies to come before them and and Present the results and have to speak to the result defend the results show how they plan to improve over time etc. So it's It's fully transparent. It's available in French English in Spanish. It comes with training for the program as a whole but also on some of the specific areas that have been developed it's a and What makes it unique is there there isn't another program out there that Is measuring performance at the site level? You'll have a lot of public reporting in our sector or in other sectors that are sort of company wide Sort of a corporate roll-up But as we know You know in all if you're being honest any mining company will tell you they have some mines that operate better than others And so you can hide Your overall perform You know your your weaker performance by and highlight your your stronger performers and this really this program essentially compels you to be totally honest and transparent about your strengths and weaknesses because you report on all your mines But then what that does too is in private provides a very strong incentive for the mines to improve their performance and we're able to show After over ten years of doing this Significant improvements and performance across all of the indicators our companies are much better today at what they do Then they were a decade ago and TSM is partly responsible for that and how Are there what are the examples you see? What companies were or we're not doing Well Well, one of the obvious one of the obvious areas is around community and Aboriginal engagement Today are in Canada our sector is seen as in the vanguard of Aboriginal inclusion Compared to other sectors it's not to say they're you know, if you don't at times have Difficult relationships sometimes with some Aboriginal communities or some companies But for the most part the industry is now regarded as a leader in this area and There's a lot of interest amongst Aboriginal groups in terms of getting involved in mining and they are getting increasingly involved in mining, but if I go back 10 15 years this was still pretty scary stuff for the sector Some were doing it But a lot we're not sure how I Remember developing TSM early on and There was a fair bit of pushback from some of the more Established mindsites, you know saying well It's easier to do this if you're developing a new project to engage with local communities But you know, we've been in Sudbury for 70 80 years or whatever it is or we've been in Timmins or we've been in Cam loops or wherever it may be You can't expect us to you know repair a relationship or start a relationship now But fast forward to today and they all have they now all have agreements with local first nations and The involvement of first nations in the mining industry in Sudbury is like it's never been before And the employment were the largest employer so things have really really turned around and I think it reflects well on the industry and Other countries around the world look at Canada and again CES leaders in this area So that's you know one obvious one Canada is also known for its leadership in tailings management We're also known We've also made a lot of progress in recent years around In terms of energy use and energy efficiency and the most Our Standards and our our set of indicators dealing with Energy are really equivalent to ISO 50,001. They're quite compatible and most of our members now essentially are achieving ISO 50,001 So it's it's it's pretty impressive what members have been able to do over the last decade Different question, but I guess the social aspect of things women How have how absent the present have women been Throughout your career and have you seen that change? So how? well here at Mac The It's always been close to 50 50% female From the very beginning and half of the vice presidents were and still are female So Half of this office is female for more Have to count now I think it's seven and five Female to to male So certainly in terms of what we do there's always been strong representation of women Since I became president we've had our first female chair of the association and Next year we'll have our second female chair. We're actually we actually have a good record of now alternating I don't know if we'll be able to continue doing that Our board has a lot more women on on it than it did when I first joined when I first joined I don't know if there were any and now there's quite a large number, but they still represent the minority And so there's still a ways to go. I've certainly seen A significant increase in the number of women I work with in this industry It I started to notice it more in Geology, but I'm seeing in sort of across the board now So it is a second we we have the data to show it. I mean it is It's still a long way from You know from a 50 50 split and You know some may question whether we'll we'll get there You know given the nature of the industry will it will it attract Enough women to get us to 50 50. I don't know The more You know the more and more technology is used probably the more and more likely that's going to be it's it's not As focused on you know heavy equipment and Though you know you'll often hear that Some of the best truck drivers in this industry are women because they take better They take better care of equipment than men do Drive more safely Yeah, so So there certainly there is a breaking down of stereotypes within the sector Occurring now how far it will go Remains to be seen, but I think there's certainly potential for it to go a lot further than it has I'm encouraged by the change that I'm seeing and that the data is showing But we still have a ways to go Compared to some of the other sectors in the natural resources area We're not doing so badly either Energy is better than we are but we're better than forestry better than fishing better than agriculture so or some types of agriculture So we're not bad But we've got a ways to go Interesting to see what do you think of the situation of the situation working I guess between government and Industry and the question is do you believe there's a disconnect between The industry the mining metal or the industry and the general public and I guess we could include maybe government in that. Yeah, I I think every sector of the Canadian economy probably thinks that to a degree Especially some of the more traditional sectors Whether it be not for resources or manufacturing They often feel that they don't they're not appreciated enough. They're not respected enough and I Take a somewhat different view. I think the reality today is our societies are now so sophisticated Information is so available that people attention span or anything is limited and It would We're kidding ourselves if we think that your average Torontonian is Going to think about mining much of their day Just like I don't think spend much much of my day thinking about the pharmaceutical sector or the telecommunications sector unless I'm Getting pissed off with my One of my devices is my cell phone Or if I'm you know having to get some prescription drug from the drug store I don't really think about other sectors the economy the way I think about mining because I work in the mining field But if you asked me generally what I think about the value of those different sectors my general view would be positive with some Reservations about certain things I may have read or heard and what we've found over the last five years of opinion polling which we've been doing Is from the public? Yeah from the general public Is that Canadians views of mining are kind of similar to what I've just described that actually a Large majority of Canadians are have a favorable impression of mining But I think the range We've asked you know the sort of the top line question is do you have a favorable or very favorable view of mining or Unfavorable or somewhat favorable and the favorable and very favorable is Has always been somewhere between as low as 73 percent or as high as 84 percent. Those are good numbers Our pollster Who's one of Canada's top? pollsters Bruce Anderson you may have seen him on When he used to be on the ad issue panel with Peter Manchbridge and he He would say for a natural resources sector. You're never going to get better than 85 percent because there's always going to be sort of 15 percent of of Society that Doesn't believe in natural resources would like to live in a world where we don't disturb the land where we Leave everything intact However realistic that may or unrealistic that may be so there's always going to be a cohort that sort of opposed you from a certain sort of More of the extreme of views and society So if 85 is sort of the top we can get and in one year we got 84 we're doing very well and What the results also show is is is they have Like I just said before about the other sectors they have they know that mining has its impacts you can't Build a mine without disturbing land Without potentially having an effect on water on wildlife. So there are environmental impacts It can be disruptive to a community if you're nearby but on balance The benefits far outweigh The costs in the vast majority of cases so their their views of mining are actually quite favorable Do they think about us regularly no are they likely to no But when asked they'll actually say yeah, it's an important sector and it's good that Canada Has a strong mining industry and they actually think governments should be doing more To support the mining sector than they currently are so it's not a bad place to be It was a surprise for our board and for our members To see these results when the first it is is yeah, because most people kind of assume and this is sort of another takeaway for us was You're inclined to follow the clippings and the media tend to cover controversies and so you think That what you're reading is representative of the broader public attitudes, but it's not Yeah, things that go well are not as sexy. No, that's right. That's right. Of course. Yeah Absolutely. Well, thank you The next question is more than mouthful. So And that's that's in your opinion. So in your opinion, are there any events? people inventions Disasters anything whatsoever You believe must be mentioned when discussing the history of the natural resources in Canada Well, no wrong answer. Yeah Well, I think in recent history and if you look at the work that we do Yeah, half Half dimension some of the tailings failures we've had the Mount Polly failure last year Some Marco in Brazil though, you know, not not Canadian And not Canadian companies was horrific horrible disaster But there were a number of sort of high-profile tailings failures in the 1990s by Canadian companies abroad oh my in Guyana Operated by Cambior Mark Hopper by Placer Dome two companies that no longer exist And one could say that the contributing factor was perhaps those feelings failures Tributing factor to the disappearance eventual disappearance Because those have such a devastating impact on a company's reputation and their bottom line But it's in response to those that we developed at Mac the what are now sort of international leading guidance on tailings management and Hot-wired that into our towards to double winding initiative So we've taken sort of the crisis of tailings failures and Turned it into a strength in terms of Canadian mining where we're now seen as leaders in this area so it's you know, it's I You know learned from Some of my mentors years ago never waste a crisis and I think the industry did not waste The crises of of seeing some of these major installations fail on them. They took them seriously they looked at what was wrong and They work really hard to try to make sure they don't happen again Thank you We'll just close with a few questions First thing what are you proudest of in your professional career? Probably the development towards stable mining That's been I Think people would expect me to say that I'm kind of identified with it It was what I I did when I first joined Mac and and now it's sort of a centerpiece of what we do and as I mentioned Now it's starting to go global so I've One of the again probably another one of the reasons why I'm still here Is because I've found in this sector a group of people really committed to doing the right thing and Wanting sometimes feeling that they're not Getting the respect they deserve for what they do. They're better than people may May think they are Which takes us back to I don't know if that's true or not, but there is that perception but certainly a group of people who Are committed to Improving the way the industry does those about its business and and towards sustainable mining stands out as a great example of that They didn't have to do this But they felt it was the right thing to do and did it in a way that made a lot of sense for business Last question and that's if you were to speak to someone much younger like a student for example What would be the most important life lesson or piece of advice who would give them looking forward not necessarily towards a natural resource industry But this was a perfect professional life Well, they should do what they're interested in Whatever that may be Life just sort of has a way of working out if you do what you like Study what you like be good at it learning how to write to me has always been It's always been one of my strengths professionally it's taken me where Where I've gone And I've always placed a high value on on that So I'd encourage people to read write learn and enjoy doing what they do and then the rest should work out Thank you. Do you have any other questions or comments? No, it's just it's odd now to be the one giving advice to people like what happened. I feel I'm getting old Well, thank you very much. Thanks. Appreciate it. Okay. Bye


If we can work, I bought my new Jeep Cherokee from Family Feet Dollars. Thanks for delivering, guys!


This lecture will be about the etalcohomology of a curve. And I'm going to take a rather unusual approach to this. So I'm not actually going to tell you what etalcohomology is before calculating the etalcohomology of a curve. So the problem is that most introductions to etalcohomology, you sort of spend large amounts of time doing abstract category theory and talking about growth and diptypologies and so on. And this is all very important, but it's also kind of a bit mind-numbing. So I'm going to skip over this and just go straight to the interesting part of the calculation. The disadvantage is that you won't actually know what etalcohomology means. So I guess this is just a sort of overview as motivation for finding the precise definition. So let me give a very quick summary of what an etal sheaf is. So an ordinary sheaf in the Zariski topology is a contrarian functor from open sets of X to sets. So here U is open and X is whatever space we are working over. And furthermore, there is some sort of covering condition that I'm not going to worry about because this is a very informal introduction. The difference between that and an etal sheaf is that an etal sheaf is a map from the etal open sets of X where this map is now an etal map and need not be injective. So obvious question is what is an etal map? And I'm not going to tell you. Probably the next lecture I'll give a sort of introduction to roughly what etal maps are. But there is sort of generalization of inclusion of open sets. So an etal sheaf is some sort of contrarian functor from these mysterious etal maps to sets. And instead of defining an etal sheaf, I'll just give you some examples. So these are the examples we're going to use. First of all, we have the constant sheaf. So here, if I'm given an abelian group A and I'm given an etal open set of X, this is just going to take the etal open set to set A, at least if U is connected. If U isn't connected, you have to fiddle around a bit more. Secondly, we have the sheaf of regular functions. So this just takes an etal open set of X to the space of regular functions on U. So this is very similar to the sheaf of regular functions in the Zariski topology, where we just map any open set U to the regular functions on U. One that we're going to use is the sheaf of invertible functions, which is, I'm used to denoting this by GM, which stands for the multiplicative group. And this takes an etal map to the units of the regular functions on it. Fourthly, we could have the sheaf mu N of Nth roots of unity. And this just takes the map etal set to the Nth roots of one in O of U. So what we want to do is to calculate the etal cohomology groups of a curve and try and show that they're very similar to the usual singular cohomology groups. So let's recall the singular cohomology groups of a curve. So this is with integer coefficients. And we're going to work over the complex numbers.  And these groups are as follows. They're Z for Q equals nought, Z to the 2G for Q equals 1, and Z for Q equals 2, and nought otherwise. Here, G is just the genus. And X is a non-singular projective curve over the complex numbers. Now, the etal cohomology groups denoted like this of a curve. Here, we're going to take coefficients mod n. And we want to show that these are Z over nZ for Q equals nought, Z over nZ for Q equals 1, so that should be to the 2G, and Z over nZ for Q equals 2. Here, n is invertible in whatever field K we're working over. And this is very important. In particular, you can't take n equals 0. You can, but you don't get this answer. And you can't take n to be divisible by the field. Otherwise, again, you get something very weird. So here, X is going to be non-singular projective curve over some field K, which will take to be algebraically closed. And the first step in calculating these groups is to find HQ of X with coefficients in GM star. So you remember this was invertible, the chief of invertible functions on X. It turns out that although this looks more complicated than the constant chief C over n, in fact, these groups are easier to calculate. And by reducing them, we'll see they get reduced to calculating a Picard variety. And what we do is we write down an exact sequence of sheaves. And the exact sequence looks like this. One goes to GM, goes to, let's call this invertible rational functions sum over X of Z. Let's explain what these are. So this stands for invertible regular functions. So in other words, if you've got any et al map, you go to X, its value on this is going to be the invertible regular functions on U. This stands for the invertible rational functions. And this stands for a copy of Z for each closed point, X of the curve X. And let's explain what's going on here. So this map here just takes a rational function for the orders of the zero or pole at each point. And what this exact sequence is saying is just saying, if you've got a rational function in here and the order at every zero and pole is zero, in other words, if it's got no zeros and poles, then it's an invertible regular function. So that's a kind of obvious statement. And this is just a sort of complicated sheath theoretic way of saying this. Now, for any short exact sequence of sheaves like this, we get a long exact sequence of cohomology groups that I will write out in a moment. And what we want to do is to calculate the cohomology groups of this from the long exact sequence knowing the cohomology groups of this and this. So we need to know what are the cohomology groups of these two objects. Well, first of all, let's look at the cohomology groups of this. We'll hear the cohomology groups. So hq of sum over z is equal to zero for q greater than naught. The reason for this is that this is just a sum, a direct sum of sheaves with support, a point, and furthermore, this point is the spectrum of an algebraically closed field. And in etel cohomology, the spectrum of an algebraically closed field, all the higher etel cohomology groups vanish. I think that should be a direct sum sign rather than a summation symbol, but never mind. So these cohomology groups are easy to figure out. Now we want to know the cohomology groups of these, and these again all vanish for q greater than naught, but this takes considerably more effort to see. So I'll sketch why the cohomology groups of this all vanish. So what we want to know is we want to work out the cohomology of x with respect to the sheaf of non-zero rational functions. And we can reduce this to working out the cohomology of the generic point of x with coefficients in the rational functions. So it's really spectrum of k where k is the field of rational functions on x. And etel cohomology of the spectrum of a field turns out to be the same as Galois cohomology. So Galois cohomology means you take the cohomology groups with respect to the Galois group of the algebraic closure of k with respect to whatever you're taking cohomology of. It turns out that etel sheaves over the spectrum of k turn out to be more or less the same as modules of the Galois group. So working out this turns out to be a problem in Galois cohomology. And we do this in several steps. So I guess step naught is to say that etel cohomology of the spectrum of field turns out to be Galois cohomology. Incidentally, we used a special case of this last time because if the k's algebraically closed, then all these Galois cohomology groups vanish for i greater than zero. So in order to work out these groups, we first used Sen's theorem, which says that suppose k is field of rational functions on a curve over k where k is algebraically closed. Then k is C1. Well, what on earth does C1 mean? Well, C1 is this funny technical term, meaning any homogenous polynomial in n variables of degree less than n has a non-zero solution or non-zero root. So for finite fields, this is the Chevalet warning theorem and Sen proved it for fields of transcendence degree one over an algebraically closed field. The next step is that a C1 if a field is C1, then it implies the Brouwer group is trivial. So what's the Brouwer group? Well, the Brouwer group is a group formed out of the central division algebras over the field. So we need the theorem of the Brouwer group, which is another of these things I'm going to skip. So in Galois cohomology, the Brouwer group turns out to be isomorphic to the Galois cohomology of k bar over k with coefficients in the non-zero elements of k. So the Brouwer group is the second cohomology. If you're wondering why we don't start with the first cohomology, the reason is very simple. Hilbert's theorem 90 says that the first cohomology is always trivial. So Sen's theorem says that the second cohomology is sometimes trivial. Thirdly, there's a theorem from Galois cohomology which says that if the Brouwer group equals one for all finite extensions, this implies that hq of k bar over k with coefficients in k bar star is equal to zero for all q greater than or equal to one. And using the correspondence between Galois cohomology and etal cohomology, this implies the etal cohomology of hq of x with coefficients in the non-zero rational functions is equal to zero for q greater than or equal to one, which is what we wanted to do. Okay, so we've proved some vanishing themes from cohomology. Now we get on to the long exact sequence of cohomology. So let's write out what the long exact sequence corresponds to the short exact sequence of sheaves. So it starts off with the zeroth cohomology of the groups in the short exact sequence. So this is going to be a sum over copies of z. And then this map here isn't necessarily onto and instead it maps onto the first cohomology.  And now we use the vanishing theorems we've proved. So all this junk vanishes using to sends them and brow groups and all that other stuff. And all this vanishes for rather trivial reasons. And so we see as a consequence that all these groups vanish. So it just leaves h0 and h1 to work out and that's very easy to work out. So h0 is just the rational functions with no zeros or poles. So this is just isomorphic to k star. And here we notice that h0 of this just means we assign an integer to every point. So these are just the divisors on the curve. That's linear combinations of points. And these are just rational functions. So the image of this is just the principal divisors. So this group here is just the principal divisors. Sorry, it's just all divisors. Modular, the principal divisors which is the divisor class group. And now we have to work out the divisor class group. And first of all, every divisor has a degree which is an integer, so that gives you a factor of z. And that's the product of z and the divisors of degree zero which are called the Picard group or Picard variety or whatever. And that has a fairly complicated structure that we'll talk about a little bit later. So the cohomology of the multiplicative group of the field can be worked out explicitly in terms of the Picard group which is the group of line bundles or the divisor class group or whatever you want to call it. Now we use that knowledge of the cohomology of the multiplicative group to work out the cohomology of z modulo nz coefficients. So first of all, we notice that the chief C over nz is isomorphic in a non-chronical way to the group of roots of unity provided n is invertible in our field K. This is the key point where n has to be invertible. And now we have the following comma exact sequence. One goes to nth roots of unity, goes to gm, goes to gm. So this is raising things to the power of n, goes to one. So this is a comma sequence. And there's one very important point here which is this map surjective. And this is surjective in the etal topology but not the Zariski topology. So in some sense, the surjectivity of this map is the main reason why we're using the etal topology instead of the Zariski topology. Much of what we've done so far works pretty much the same way in the Zariski topology. For instance, we could calculate the cohomology of x of coefficients in gm and we get the same answer. It just gives us something involving the Picard group. In fact, calculating this is much easier in the Zariski topology because you remember calculating h1 of this group here was really quite difficult in the etal topology. We had to use to send theorem and Brau groups and whatever. In the Zariski topology, this group here is really easy to calculate and it's very easy to see at zero. The problem is that the same very easy argument that shows that zero also shows that the cohomology of this group vanishes in the Zariski topology which is not what we want at all. So the surjectivity of this map is essentially related to the fact that the map taking Z to Z to the n is an etal map from K star to K star. So the surjectivity of this is a sort of key point that you need to pay attention to. Now what we do is we look at the long exact sequence of this. So we know the cohomology of these two groups so the long exact sequence is going to give us information about the cohomology of this which is what we want. So let's take a look. We get nought goes to h1, so h0 of mu n, goes to h0 of gm. I'm missing out x here because I'm getting bored of writing it out. Goes to h0 of gm and this is multiplication by n and then here we have h1 of mu n goes to h1 of gm goes to times n h1 of gm goes to h2 of mu n and now this goes to h2 of gm and everything from this point onwards is just zero. So what can we see from this? Well, first of all, we notice that all these higher groups are equal to zero because they just fit into this exact sequence of zeroes in front of them and behind them. Now we can recall what these groups are. So this group here was just the multiplicative group of k and this group here was the Picard group z times pic zero, z times pic zero. So if we write this out a little bit more neatly in one line so we can see what's going on, we get the following. We get the following, we have nought goes to h0 of mu n goes to k star goes to n k star goes to h1 of mu n goes to Picard group goes to n, I guess that should be z times pic zero goes to h2 of mu n goes to zero. And now let's think about this a bit. This map here is surjective. So this map here is the zero map and this gives us the rather uninteresting information that this group here is just a group of nth roots of unity which we already knew. Now since this map is zero, this group here is the kernel of the map from z times pic zero to itself. So it's the kernel of the of the map saying x to n times x. Now the kernel of the map taking z to n z is zero so we can forget about that and we need to know the group of elements of order n in the in the Picard variety and this takes a fair amount of calculation. This is in fact an abelian variety of dimension equal to g as shown by v in his work on the v conjectures and the elements of order n provided n is invertible is isomorphic to z over nz to the 2g. This takes a fair amount of work as I'm just going to quote. Now finally this group here well the map from pic zero to pic zero is onto surjective again you need to think about abelian varieties in order to prove this so we're left with the map from z to z which is multiplication by n so all we left with here is the group z modulo nz so finally we see that h zero of mu n is equal to z isomorphic to mu n h one of mu n is isomorphic to z modulo nz 2g and h2 of mu n is isomorphic to z over nz actually that probably shouldn't be a z over nz but never mind if yeah we since we're just assuming mu n is isomorphic to z modulo nz this doesn't really quite matter how we write this and I guess it shows that hq of mu n is equal to naught for q greater than 2 so this is the result we want remembering that mu n is isomorphic to z over nz so that gives you the etalc homology of a curve this allows you to get hold of etalc homology of high dimensional varieties because what you can do is you can map an n dimensional variety and the fibers will be curves and you can get hold of the co homology of the fibers by using this result they might be singular so you need to do a bit of extra work and then you can apply spectral sequences to relate the co homology of your variety to co homology of the base of the fibers and so using this basic result about curves you can sort of climb up to etalc homology of higher dimensional varieties okay well one thing that was really rather seriously missing in this lecture was I never actually explained what an etal map or an etal sheaf was so next lecture I plan to say a little bit about what an etal morphism of varieties or schemes looks like