Hi, Tom Stewart here with Cleaning Business Today, got my partner Liz Trotter, hey Liz, and a very special guest today, Joe Walsh. Joe has some really awesome information he's going to be sharing with us on the latest developments with PPP, the Payroll Protection Plan and I guess some of the work he's been doing with some of our legislators and I guess the press as well to get some maybe gaps in understanding close to hopefully PPP will work better for us than what it does now. I want to swing back around to tell it like it is because on Friday we were talking about needing to decide between does tax credits maybe make more sense than PPP and building a calculator to help us figure that out. Well, a couple of things have happened since we had our call on Friday. Remember what we say, you know, like that's what the stuff happens in 24 hours. Well, this is nothing different, especially when you go over a weekend. There are two ways that you can qualify for the tax credits.  You have a big drop in revenue from the prior year's quarter, I believe what it is. The small print and all of that means though that if you qualify you're not necessarily qualified for the entire year through January. You have to basically meet the qualifications each and every quarter and Joe kind of helped me out with this too because I think your CPA shared that you can kind of stay in the range where you're qualified as long as your revenue doesn't hit 80% of where it was the prior year's quarter. Prior year, that's right. But when you start looking at the numbers like that it's like you're not even guaranteed to get it for the full year and hopefully you wouldn't because you know by the time you get to the second half of the year hopefully you got enough revenue going that you would be in a range where you wouldn't be qualifying. So the short story is the PPP gives you the money up front which is really awesome and it looks like the federal government is really pushing people towards that. So in some regards you don't want to want to swim upstream on that and with the uncertainty of the tax credit it was our judgment that building a spreadsheet to verify something that we seem to already know just based upon where everything's pushing us made no sense. So you know we're believing for anybody in the house cleaning industry PPP would make more sense especially with some of the more later developments that Joe's going to be sharing with us here because he's actually been a heck of a leader for us in the industry bringing to light that there's some gaps in the logic of PPP and how it's really going to work for a restaurant or a house cleaning business or anybody who wants to bring their employees back but doesn't really have any viable work to do at the moment. So Joe you want to share with us a little bit about what's been going on and what you've been doing? Yeah so for the PPP the Payroll Protection Program you just a quick review it's a loan and there's a portion of the loan that's forgivable. The portion of the loan that you use to cover payroll costs is forgivable and they'll forgive the amount equivalent to the first eight weeks of your payroll cost from loan distribution. So if you maintain 100% employment if you don't maintain 100% employment they prorate the amount that they'll forgive of the loan based on the percentage of the numbers of employees that you have. Okay so it's this is important to understand that you know you'll still get some back if you don't reach 100% employment but you're gonna only get a percentage back. Okay so what does this mean though for us if you are a business that has stayed open and been able to maintain full employment or close to full employment the PPP makes a lot of sense. It especially makes sense if you're a professional in more of a white collar work environment where people can work remotely and things like that. So take my accountant for example my accountant is a small practice he's got seven employees he's been able to keep them all in the payroll but their revenues have dropped off precipitously because people are not doing their taxes right now because everything's on hold and people aren't able to pay him because people are having to close and so he has applied for the PPP and my accountant will most likely get 100% of his payroll costs for eight weeks covered to kind of help cover the period where things have really slowed down and for someone like him this could be the difference between a profitable year and a marginal year and so I'm not questioning the value of the program itself what I'm saying is if you compare that to someone who is in my situation or Tom's situation and Liz are you closed I actually am not aware of that you're not closed okay so if you're in this if you are though someone who had to close either because of a government order or because so many of your customers canceled you know like a drop in business if I have to take disbursement of that loan now which I'm being told to do because the funds are going to run out then my eight weeks starts now I don't have any employees to pay because we're not cleaning anything so I'm not going to get it's really unlikely that by eight weeks from now I'm going to be at 100% employment so because of that I'm only going to get whatever small percentage of employees I have back I'm going to get a small percentage of their pay forgiven so as someone who's had to close and has been impacted a lot more severely than say my tax accountant I'm going to get much less in the form of a forgivable loan which is kind of like a grant and much more of it is going to end up being alone and I'm going to have to pay back so that's a hole in the logic of the program because it's it's like skipping over those of us that have had to close and focusing the most of the forgiveness on those that can stay open so when you think John even for a lot of companies that are open they've lost a material amount of their revenues so I mean they would doesn't really make as much sense for them as what I think the legislators were thinking when they wrote the law the way they did right and even you know in the cleaning business you know I've been we've been talking about this now for a week kind of ad nauseam I feel like and in the cleaning business they you know let's say you've had to lay off half your people well how are you going to bring them back if there's no customers there so some people say well you just pay them to sit at home until the demand returns okay well that is okay I guess but with the way that the unemployment insurance legislation that has come down is working you're going to have to start paying the people that you have working a lot more money to have them making more money than they would be just being at home and being unemployed so that creates a whole other aspect of this and you know we would almost need that PPP money so we can supplement our employees wages so that those who are working are making more money than those who are sitting at home as a business owner I don't want to be put in the position of having to tell my employees you need to come back to work for less money than you would make sitting at home it's just putting me in a terrible position and I don't think that the policymakers intended that but it's the way that it's all playing out and it's you know it's a gap that has to be addressed so so Joe the gap that you're addressing then is it also going to deal with so like the medical all of the medical workers everybody that's out there on the front lines they're all working and they're making their same wage that they've always made but the people that are sitting at home they're actually going to be making an extra $2,400 a month so is that what you're dealing with is that addressing that gap on top of the PPP or are you just focusing on the PPP currently well right now my focus is just well my my focus is just on the PPP and how it affects businesses like ours so you know it was what I did was I put I kind of got together with a a a fellow business owner in my city who also happens to be our state representative she owns a brewery and they make really good beer actually and she's she's a lawyer by trade originally and is now a state senator and and owns a really well respected business in town and is looking at the same issue and she is very well connected with a bunch of other people in the hospitality and restaurant industry and there's this growing consensus that wait a minute this isn't really working for us like we're watching all these other businesses get a bunch of loan forgiveness and we're kind of being left in the dust and so you know those of us that have had to close are in the same are in the same boat so the focus is on this sort of hospitality you know businesses that are non-essential that are being forced to close um or maybe your business is deemed essential but there's been such an evaporation and demand that you haven't been able to stay open um either way the the outcome is the same because you're closed you can't pay people um to do that and you've got no revenue coming in um there's no demand there so and the employees are better off just sitting at home right but why are what Liz is suggesting is mention the fact that the six hundred dollar federal unemployment on top of the state benefit is working against us too I mean why is while we're at it it is because then what do you say to the first responders who are making less than twenty six bucks an hour your local EMT is not making twenty six dollars an hour it's crazy and and neither are the people a lot of the people working in the hospital so you know that's not right either I mean I'm not it's just it's like a double whammy though for small businesses it is I think you know I'm not approaching this in a way that's you know I'm not this isn't a partisan thing this isn't something where I'm just trying to raise the issue and make as many people aware of it as possible and in in in my mind and in the mind of you know my state representative and I agree with her the best way to do that right now is to just go straight to the press because we have to get the word out you know I mean we've all contacted our state legislatures sorry our um national delegation and shared the story but they're more overwhelmed probably than anyone else right now and the story needs to get out to the public that like this isn't going to work the way it's intended to work I love that idea let me work on that like you are witnessing it developing in real time like my phone is ringing over here and it's a reporter I think from the Bangor Daily News trying to call me um uh but which is part of the reason I have to hop off the call and just a little bit but um yeah let's do a press release and we'll get some language together and and then we can send it out to everyone and you can contact your local media you know say hey this is this is what's happening on the front lines of this the media want to tell this story and the policymakers want this money to get into the right hands I really just think this is something that just if we just raise awareness we don't have to be hysterical but we just raise awareness and just say hey this is kind of how it's coming down you know it's not really working that well and part of is getting out of the right hands and the other part of it is making the rules such that it can actually be productive be effective they're creating a scenario where you know it makes no sense just to hire people if there's nothing being produced if there's no economic value being generated and if right if you're a restaurant you don't have any any guests what's the point if you're in the cleaning business you don't have any jobs what's what's the point right and you know I've heard some people say that part of the thinking is oh they want you to pay people to sit at home in their couch so that they're spooled up and ready to go I I've never seen it anywhere that that was the intent if that actually was the intent I'd love for someone to show me like point that to me like what it seems to me the intent of the law is to get people working not to pay people to stay home we already have funds allocated for that we already have the unemployment funds have already been allocated for that so you know so the simple change I'm suggesting is rather than say it's an eight-week period from loan disbursement give us eight weeks but let us choose the eight weeks give us like a four month period that we can say okay sometime in this four month you have to choose your eight weeks and that's what we're going to base your loan forgiveness on because a lot of us are just going to need a little bit more time to get ramped up it's just too early the government's still telling us to stay home you know we still need to pay our rent and other things give us the ability to do that for that period you know the from day one from day one give us the money now but we need to be able to need more flexibility in the eight weeks that's all so what about this idea Joe that I'm hearing people are saying yeah they want to give you that eight weeks now because they want you to put the people to work now but they want you to find other ways be creative with the way that you put them to work maybe get them to do some marketing for your company or something so that when June 30th kids that went supposedly that's their their date right now right so that you can you'll have enough business that people will come to you and you'll be able to school it quickly that's I think that I I guess I've never seen that any I again I haven't seen any sources say that that's what they they want you to do and by I mean the the senate committee that drafted the legislation I mean it I've not read that that's that they're kind of saying do anything you can to get them back on payroll um in what I see is people reading into the law and and sort of signing that to it also I think we all know I can only put so many people to work hanging up flyers I've got 30 frontline staff you know 30 house cleaners I can't put 30 people on the street hanging flyers up until my customers come back or even 10 or even you know so that's just not I don't believe that was the intent first of all because it just doesn't make any sense operationally like from an operations perspective I do it if the government said hey you know be a patriot hire people like here's some money okay but that's not what I'm being told I'm being told like what I take from it is we want you to open your business back up but yeah on the other hand we're kind of being told in some states you can't or maybe we just don't have the demand there to do it and so you know if that's the case we just need more time is all I think you're I think you're right Joe that makes sense to me as well I I what I've heard is just a lot of people responding with different things that just trying to figure out what it could possibly mean because the way it's written right now doesn't seem to make sense well right so you know that's why I'm trying to go to the source and find out you know if there is some credibility to this oh what we really want you to do is pay people to sit at home that I want to see where that was written you know the scary part about that is you could you could do that I mean you could you know invest in training or door hangers on you know I'm sure there's ways that you could could could put people on the payroll and spend all the money but if something happens and you get down to June 30th and you don't have every position filled I mean that's a scary thing if you weren't really generating generating any revenue off of all those salary dollars and something happens at the end and you find out that you aren't getting the hundred percent of the grant that you were planning on because you know you spend a ton of payroll money and really had and then you may have to lay people off again okay which is like a terrible thing to put employees through especially considering they could have just stayed at home and made a thousand bucks a week in my case and do we know do we know how people have to be employed after June 30th in order to meet that requirement there's no language that I know there's no language that I know of about needing to stay past June 30th it's just that you're going to be laying off employees in what could be a different environment by then like right now my state has a temporary like if you lay people off because of COVID-19 it doesn't hit your unemployment insurance experience rating so in other words we're not paying into that but if I have to lay them off a second time by that time maybe they've lifted the the the temporary emergency order and now I am paying unemployment insurance for those people you know so it's it's it's risky and I I I guess I find it hard to believe that that was the intent when they drafted the law I feel like if that was the intent we would have been reading about it and it also just doesn't seem to make any sense that's what the unemployment insurance is for all of this happens so very fast and there's so many ways for unintended consequences I I agree I just just think that this was was an unintended unintended consequence that that went by unnoticed and to some degree I have to think it's on the radar screen now but there's so much moving at the same time that you know I don't I don't know how I fix all this at once yeah no I you know I agree and that's why I'm my approach is is measured and and thoughtful and consider it that you know the the policymakers have been working around the clock to to make this happen and there's bound to be mistakes and I think we need to work together to figure out what the mistakes are and just you know kindly but firmly point out the flaws and like where holes need to be addressed and um like I said I think the press is the fastest way to get that out there sorry what sorry I think it's smart to remember we're talking I think it was smart to remember that if they put two trillion dollars out that they're doing it because they're trying to build us up not crush us so I just just keeping that in mind that it makes a lot more sense to move forward you actually teach this Liz assume positive intent okay and and I would say just beyond the positive intent if you just look at the logic of the situation absolutely they're trying to help us they're not trying to to you know not help us so destroy us nobody wants us to fail no they don't so we have to help them help us yeah yeah uh so um Linda has a question she wants to know should we even apply for the ppp yet or and hope that it works out or should we wait what what do you think um uh tom you can weigh in on this I my opinion is apply you can always say no if excuse me you can always say no to the money if over the next few days developments come out that you know give your reason to believe it's better to wait the reason to apply now is at as of today at 5 25 p.m the funding is limited now there's encouraging developments tom you forwarded me an article in the wall street journal that was very good um about you know the the treasury is trying to free up more money to go into this program but as of today at 5 25 p.m it's limited to 357 billion or something which is going to go away like that so it's better to get it in now and if you can always say no to it the the treasury said they're going to go ahead and um you request Steve Mnuchin the head of the treasury said that you know they're going to go back for more money if they need it Nancy Pelosi said she'd you know prove it and sign off on it so you'd think that we get more money but at the same time the federal reserve had made a statement today where they're going to start buying this debt back from the banks that are making these sba loans basically freeing them up to loan even more money so there's a lot happening there to get more money but um you know we had a discussion earlier today about you know sometimes it doesn't pay to be on the bleeding end just some of these things like uh with the uh emergency loan i remember a couple of weeks ago we were all printing these forms out and getting them all ready to upload and we come back monday morning and all that was gone and you know the rules for ppp have changed a couple of times over the last few days but um i think we're to the point now with ppp that the banks are are taking the applications and all of that at least at this point seems to be working now that now would be a be a good time to do it i don't think that you're going to be wasting your energy i think that that that that you know initial part of it anyways been figured out and you might as well go ahead and get in line like like joe said when it really gets down to okay you've been approved and this is the amount of money you'll have more information then than you do now and you'll be able to make a decision if you want to take those monies or not yep my only concern on that is uh you apply now you get approved now and then it begins those eight weeks if there's no adjustment to to the way these monies are being dispersed you can't say or can you say no i don't want this and then wait and play again in two weeks because one of the things that is listed on the criteria is that you have not applied for another one of these loans that's a good question and i do and in terms of could i apply deny the money and apply again later uh i i would think that the intent of that is that you're not applying for more than one at the same time and receiving disbursement for more than one at the same time because they're being dispersed through banks you could conceivably apply for one at bank of america one at you know well's fargo and get both of them okay and so what they're saying is yeah what you're doing that but you know i would ask my bank for guidance um could i cancel this application and reapply in two weeks it would seem to me again i would talk to them about but you know your your point is as well taken les and i guess we've you know contemplated that and that kind of gets into you know joe's efforts to to to bring this whole dilemma you know took to the press and shed some light on it um ideally we would have that eight-week window further down the road so you know there there could be some some logic in in in using that strategy it's just you know the risk of of how long the program's gonna gonna be there and will the money's actually be there in spite of we've heard a lot of things that you know the the ten thousand dollar grant which may or may not you know we can be happening at the twelve hundred dollars that was going to be in your bank by now but but it's not so you know i don't with all good intent i don't think that people are intentionally misleading us but this is just rapidly changing and you have to weigh yeah rather have it later but if our weight is there a chance i won't get it at all at all yeah yeah and that's where yeah yeah i'm just reading what rebecca has to say she just applied to the bigger bank yet i think i think a lot of people are finding that the banks know that they have a way to do it online etc smaller banks are still a little clueless um netasha wants to know if we don't use money can we send it back yep that's the way it is so far and you're you're paying one percent interest on it you're paying one percent interest so even if you just keep take the money sit on it for a few months and ended up having to give most of it back you're gonna pay very little interest on it yeah you want to you want to my one piece of advice would be you want to take that money and put it like in a in a in a savings account a checking account and try very hard not to spend it until you really have your strategy and know what you're doing because it's really cheap money it's the closest thing to free money you're ever going to get from an interest standpoint and don't be in a big hurry to give it back i mean it doesn't come to me two or until two years and again that's the way the rules are written now all of that can change i can't imagine they wouldn't necessarily raise the interest rate but i could see them maybe extending the amortization i don't know i haven't heard that but i mean who knows how this could could could could could evolve to to potential meteor benefit down the road yep yep um are there any other questions um for this particular joe thank you for for for for taking a slice out of you know your your busy day i know you're doing some stuff right now so get out there and um you know get the get the word out for all of our benefits okay and definitely um yeah and list thank you for the press release suggestion and we're gonna i'm gonna get something together so i'll you know we'll we'll post it um i'll let you guys know and we'll we'll get something out there yeah once you get that we'll put it i mean we'll put it a whole bunch of places and the resources here and we'll get it out we'll do a newsletter and send it out to everybody yep okay all right excellent thank you guys thanks joe talk to you soon yep hi joe hey tom i remembered that um you were going to tell it like it is around the different training programs that were available for um your i saw you the light bulb just go on there tom wow i know that g-back which is the global bio something i forget the acronym but anyway it's part of issa and affiliated with with rc has a training program coming out that um for house cleaning comes for arxie members in particular there's going to be a discount where i have it from a very reliable source we're going to be able to take that class for forty nine dollars and i think the retail price is like three hundred i heard that was come out today it uh i saw it was coming out today it did there's a press release out on it that i got along with with some some of the cbt gets all these press releases i don't know if it's formally been announced yet but um it is it it's going to be happening and i think it's going to be relatively soon well i've been seeing a lot of different training programs coming out tom um this seems like everywhere i look i'm seeing another somebody has another certified training program what what do you think about these are these valuable um most of them are pretty inexpensive do you think it makes sense in the this climate to take as many of those as you can and get as much certification as you can or or do you want to try and find the certification that actually has some chops behind it or what do you think that yeah i would be you know training is good but not all training is the same so you really need to to to look at you know the the learning objectives from the training you know what's the syllabus what are what are they actually going to be training and how does that fit into your particular business and if there's a certification involved and certifications really you know in order for for certification to be of value it needs to be recognized by the general community your your as having value having merit and all of these things you need to consider as well i mean i'm not in a position to say yes or no to any one particular program but um you know you want to be you want to be strategic about it you need to be thinking about strategically what do you want your business to be you know um the g-back for for like forty nine dollars you can learn a lot about you know how to do forensic cleaning and what you know the deep cleans and all of the the the the important stuff that that the people that are doing the the heavy duty you know disaster worker are doing or at least that's my my quick understanding of of what that is is about i'll share my screen here and i'll show you the the the press release maybe we can read it together how about that i didn't do that right here we go can you guys see that at all yep we can at least i can um so what are we doing here front line cleanings essential all on course video presentation patty is really good first step includes infant origin symptoms treatment of covid as well as information responsible for cleaning and disinfecting is there be contaminated we're armed the knowledge needed to respond to recover my husband in the workplace okay i love that that was good job y'all you know it's it isn't crystal clear to me what the what the what the syllabus is but it sounds like that this is gonna give you a lot of the science which is important to have and you know a basic understanding of of you know what the what the forensic you know deep cleaning is about and even if you don't do that most of us don't most of us aren't prepared to do it i think it's really good that we have a basic understanding of that because you know you're going to get a phone call and somebody's going to say that hey you know we have this office space here and you know two people had covid 19 and want you to come clean it up for us then you'll know how to do a risk assessment you'll understand what it would take to do that responsibly and you know you might say hey i don't do that type of work but you're doing it from an informed perspective rather than just grabbing you know your cleaning caddy and going over there the way you went any other home because you didn't have the information to know any better right i would i would i would say for forty nine dollars this is a deal you notice it says 150 bucks but i've got it from an informed perspective who would know what they're talking about saying that uh there's going to be a discount coming out for uh rxy members that we can do it for forty nine which is really pretty cool yep that it seems like a no-brainer for forty nine dollars for sure i heard that somebody and i'm not sure who i uh Sharon Cowan Debbie Sardone maybe is putting out an hct light program have you heard anything about that heard it was happening or maybe it did happen did it happen last week friday did already happen friday saturday maybe oh did i really mess it well i could be wrong i could be wrong on that i i was talking to somebody who was telling me it was happening friday saturday but i don't know for sure and i haven't talked to bruce like a week or so i talked to bruce about a week ago and he bruce vance was was actually going to be teaching the course and we're going to be doing it online and it was uh basically the same material that is in the hct manual this uh you know this guy right here yeah there was no certification you know test to go along with it but but with the same information and um that's a good class that you got the invite and that it did happen oh well i i'm thinking that that would have been a good thing to have all of my people that were not working that to do the people that are you know laid off right now i have i have a good chunk of people that are laid off so okay that's a lot more that's a great program i think getting the information is more in my mind the information is more important than the certification but i do think that moving forward the certifications are going to matter more than they ever have in the past to our clients i think they're going to be looking for once they know to look for it and that they're out there they're going to start looking more than they ever have we were talking a little bit last week about the need for some some specific training for for house cleaning companies to deal on a COVID-19 world not necessarily how to do the uh you know the deep clean uh forensic type cleaning but just you know how do we keep ourselves safe how do we we make sure that we're creating value for our clients and and doing all this in a responsible way um you know we could do that here and in in with this group if if we thought that would uh that would be useful i i don't see how it couldn't be useful how how do we go about doing that how do we go about getting that i don't think anybody's going to turn down free free training i don't know i'll share something i just jotted down this weekend and it's not complete yet but just to give you an idea and i'm not sharing my screen yet but i'm working on it bang okay what might make sense tom if you already have some sort of a an idea for the free training um maybe these calls could transition into the training and plus you know 10 15 minutes of q and a can you guys see my screen yeah this is very soft and squishy at the moment and needs to be refined but you know just explaining what COVID-19 is and symptoms and you know who may have the disease and the type of questions you need to ask your your clients your prospective clients and you know your your your cleaning technicians as well everybody's working for you you need to ask retain if anybody may have been exposed to it uh you know how does it spread and a lot of information pertaining to that how do we stay safe oh you know the hand wash sanitize kind of get into that and let me let me back up i'm visualizing this is something that you would want your cleaning technicians to see this that would be you know i feel it's really important that we we have something that your house cleaning technicians would have all this information share that with them in a way where where it would be actionable to them um how do we professionally clean a home and stay safe you know everything you know above plus you know PPE and you know understand break the chain of infection how do we break the chain of infection kind of getting into that and what sanitizing disinfecting and so forth how do we uh how do we need to know or what do we need to know before cleaning a home during this crisis you know questions that we need to be asking what is the scope of work and what does the scope of work like look like in the COVID-19 world um want to talk about the tools that we use hardware and software software basically are towels and mops and the hardware is everything else and how do we use them how do we clean them how do we care for them uh what cleaning products do we use and talk about about those a little bit remember uh chat Liz from uh HCT training yeah one of my favorite takeaways actually chemical chemical heat agitate and time and and what that means to us how do we know when the scope of work is met um well what do we do after meeting the scope of work you know we still got to clean up our equipment and you know as individuals we need to be washing our hands we were technicians and taking some other precautions how do we handle the mops and so forth that we in towels that we use you know we want to we could could talk a little about the deep cleaning or the forensic cleaning just to kind of give perspective we might have questions about misters and foggers I don't know some of this is just like I said these are just random notes but those are some some some possibilities that that that we could take some time and either just do a deep dive in one day for for a few hours or spread that out a little bit of time over a number of days if we're doing it for cleaning technicians I think if we did it all in one block and if it'd be recorded it would be something that that we could all get our our cleaning technicians to say it's going to be non-prescriptive we're not going to say use this product or use this tool or use this cleaner but everybody's going to walk away knowing why it's really important to wash our hands and knowing the difference between sanitizing and disinfecting and knowing the basics that we need to know in order to to do this safely and responsibly what do you think I love the idea of getting the education into the the people into the hands of and into the minds of the people that are actually the front lines going out there and actually cleaning the homes I think that's awesome um I would like it if we could figure out some way to get a certification around it and CKI certification I don't know what right don't even have a clue of how how that could happen but um yeah Rebecca Kimberly Kelly they're all saying they they love that idea I love it too I just um I do think that that certification piece is going to be important to people um at some point in the near future I guess it's not it's nowhere near as important to the cleaning business as having the people that are doing the work knowing what they're doing and and understanding it to the degree that they want to do it so part of part of the big struggle here is when the people don't understand don't have a clear why around why around why they're doing these things and and all of the stuff that's behind the scenes that it just don't understand it it's hard for them to continue cleaning washing their hands doing all of the important things for the long haul it's easy to fall back into old patterns until they understand you know why it's so important so I really love the idea and the information into the clean professional scans the technician scans on people yeah yeah I know yeah um a lot of people would like it Tom not just not just you and me and you know we might come off with we might come up with some type of quiz um you know I guess there's a it used to be a standard for training that I don't know if it's out there anymore called cleaning industry training standard and they use the term knowledge checks which is basically just a little quick mini quizzes but you know we can have some first questions in have a quiz or something at the end and if everybody you know did well on that there's some type of certificate of completion or something I mean it's not it's not like the nation it's not a formal you know peer reviewed whatever but at least it would be be something that would you know represent that somebody participating in the class and took a quiz at the end and showed you know that they had you know walked away with the with the knowledge that was intended to be gained from the program and pretty much that's what we're seeing everywhere right now Tom that's that's the certification that everybody is getting you know all these different places they're all having different certifications there we're not talking HTT level certification just you know I got this information I paid attention I learned all the answers and check you know I and I think it would be helpful for especially for our technicians because they also really like to get that certificate of completion saying that they did learn this stuff and they like to show that they learned it too they're going to want to show the owners of their companies look I told them to watch this I did I learned stuff we could we could do that we could we could put it online and you know if they they participated in the class and if they and whoever whoever just based in the class they complete the the test and you know they yeah meet whatever the requirement is that the test would but we get a certificate of completion we can do that yeah cool okay I love it when do how do we start when do we start wow what do we need to do I'm taking this on you and me when would be what so this is going to be something that we would do in in in in in in one slug right well we could or we could just use the same time frame time period because there's no reason why people couldn't go to cleaning business today and watch a half hour and then another half hour and another half hour and another half hour okay or 45 minute just break it up a little bit each day yeah well so we're on this we're already doing this for free for an hour every day here anyway why not huh that's what they can we're gonna we're here every day for an hour anyway we're doing this for free anyway we might as well be giving that's what I'm saying maybe half hour 45 minutes you know 15 minutes of whatever is new because there's still these new stuff keep coming up all the time okay right and then do this I think we could be ready I love it we could be we could be ready to start by Thursday okay all right let's start we can start Thursday that's soon enough I I hope that way it would give everybody an opportunity to talk to to their their technicians and kind of get everybody you know kind of feeling on on what we're doing here this would be for the benefit of this I mean we'll have all our castle keepers technicians dialed into this too I'm not stupid Tom I know that's why we're doing it because we want our people to all learn all of this stuff I was kind of the genesis actually because we were doing all of this because this is what we wanted to do it's like well we're gonna do it why don't we just go ahead and share it with everybody so yeah yeah we're all right along together on this yeah absolutely okay start on Thursday that sounds great um all right you guys everybody on this call let everybody know we're going to do free training and this is what do we want to call this training COVID-19 cleaning in a COVID-19 world cleaning in a COVID-19 world and it won't just be for COVID-19 and y'all it will be information that's applicable to any of new new things that we're having to deal with out there it'll what what are the things Tom what are we calling pathogens germs pathogens that's good yeah yeah but you know all of you know we're not gonna get into I mean we'll explain you know what's the difference between a bacteria and a spore and a virus and just take a real quick pass at that but you know we're not going to get into a lot of detail and and and you know how you how you deal with with every pathogen out there because the one that we're concerned about at the moment is you know the whole COVID-19 thing so at least at this pass if we're having fun doing this and we can go back and get more jump because there's a lot of stuff that we're skipping over that you really need to know in the world of being a professional house cleaner that's not mission critical to to the task at hand in terms of dealing with with with COVID-19 so and we can we can get broader later Kelly hit the nail on the head right there Tom emerging pathogen yeah that's all the new scary stuff that people aren't prepared to deal with yet so I think it's great okay you want to come say hi who's there somebody's no school right now huh oh i guess i better have an idea what training program she's gonna be working on yeah she's my helper she's time she's time's a little helper this is my my daughter Kate she's a freshman at Clemson this year and I guess she's at home for the rest of the semester or online learning you get to do with me for weeks at a time in vice versa it's a bonus yeah um Heather is saying she loves the idea of herself being certified but maybe not on this platform okay so this is the platform that we're probably used to right now just for this we want to get some free training out there but Heather Heather hit us up if you got you know some other ideas as to what we could do and how we could create more value with this I mean we're already trained get the education into the hands of the people that need it the frontline people that that's our goal here you remember you remember like the $10,000 grant that was going to be in our bank account in three days well we're actually going to try to at least get this out within three days that's uh we're actually going to you mean the advance you mean the loan advance well yeah the program formally known as grant um I can't wait for Joe to get them all straightened out yeah that's gonna be awesome what were you saying Liz um Heather was saying she hit us up with a personal message and I was saying thank you to Crystal as well she was saying thank you for being leaders and being forgiving I've saying thank you to her she's doing the same right she's also one of the people this whole thing makes me feel grounded in some way I mean just the whole world has changed and you know it was like today's Monday but it could be Saturday it could be Friday doesn't really matter somebody asked me how's my weekend it's like it's like any other day now it's just a blur and um I don't know just being able this is this is gives some some sense of of of of community and makes it makes us feel good true it's true helping everybody yep I don't know what you said but you made Heather die laughing of why oh the day sounds funny I guess rather laugh and cry right yeah very true very true very true all right anything else before we anybody have anything they want to know uh for Tom what he wants that they want him to tell like it is tomorrow I would really love to hear you tell us at some point in time Tom that somebody somewhere got some money from someone I keep hearing about all this money but I sure haven't heard of anybody getting any of it yet we've got a few folks that have gotten unemployment checks that we that we for a load two weeks ago which is unemployment the best information we had on that and this was Friday that that was a well you were sharing that in Washington the actual you have to apply for it right the six hundred dollars yeah yeah in the application three weeks out right yeah and as we as we I heard go ahead I heard the 19th was the soonest anyone could expect any money when they expected that was on that document no no they could already they already applied on the first but the soonest anyone could expect any money would be the 19th was the very soonest I don't know I said Kimberley says amen oh wow Crystal Ham has a friend that got her PPP debunked today hard wow that fast so wow yeah I've had to have applied for it maybe Friday a few is but dang that is awesome that's why they're already that's why they're already low on funds they're already giving it out okay good to know crystal thanks for that uh okay so Rebecca says this is the business owner's group correct I think that is where she is concerned and if we give all our staff access right now I can pick and choose which sessions I share with them so they might not want to share everything a point I mean we're talking about some stuff here that we probably wouldn't want but we got a couple days to think about this we're not going to start till Thursday I mean we could and we could do we got you know I don't know that's a good point let's let's let's let's chew on that a little bit but we're going to start doing the uh the the the science base you know cleaning training for for for COVID-19 by Thursday if we do it on this call or if we do it on some other platform I don't know we'll we'll we'll we'll have some discussion we'll we'll come up with a good idea on that you know the next day or so a lot of moving parts what I mean to do all right anything else anybody else have a tell it like it is topic that they would like Tom to investigate I like to keep him working he gets you know I've been working from home I'm getting soft here you gotta gotta keep me on okay so cleaning business today that's uh what we got here and we get a press release I think our next newsletter is going to have the press release in it as soon as we get that we'll get that out hopefully hopefully as soon as tomorrow if you want to get a copy of that press release you need to make sure that you subscribe and if you get our other newsletters then you have if you don't get our newsletters then you'd want to want to come here and subscribe they've got a link to our resources bang it's a forward slash corona coronavirus dash downloads and I'll drop that in our thing here you're welcome Bridget thanks for coming and hanging out with us every day and also a reminder you saw where Tom just was in the links if you haven't gone there go there check it out there's a lot of good stuff there yeah clicking on stuff right okay guys well thank you you guys stay safe and we'll see you tomorrow five o'clock in your story see you tomorrow rebecca bye


Okay, so what I am going to do now is tell you few more facts about the behaviour of a function in a neighbourhood of a critical point. So let me recall what we have seen in the last lecture, so you see we have the following situation, you have the function W equal to f of z and with well z0 is a critical point of f of order m-1 and we interpret it as z0 is a 0 of order m of f of z-w0 where w0 is f of z0 is a critical value, okay. And of course we choose rho greater than 0 such that the 0 of f of z-w0 namely z0 is isolated there in a disc centred at z0 radius rho, okay. So f of z-w0 is not equal to 0 for 0 strictly less than mod z-z0 strictly less than or equal to rho and choose or let and of course we have delta is the minimum over mod z-z0 is equal to rho of mod of f of z-w0 and then what we do is that we have this diagram if you recall where we took this disc in the complex plane the z plane centred at z0 radius rho, alright and then we are looking at this map this map is into so let me use some space above because I want to draw something above. So this is into the w plane and z0 goes to a point w0 and I am looking at this disc centred at w0 and radius delta where delta is chosen like this, okay and the fact is that so the function goes like this and what is happening is that we have so and this whole transformation is broken down in such a way so that it conformally looks like z going to z power n, okay. So how it is broken down is that you have first of all a change of variable I do not know what I called it so it is z going to zeta which is h of z if so please let me know if this notation is conflicting, okay I think it was h of z and then so this goes into the in the copy of the complex plane which is now the zeta plane and the image of this disc is something that looks like a disc, okay because h where of course we have set we have made the following definitions we write f of z minus f of z0 is z minus z0 to the power of m into g of z, g of z0 is not equal to 0, okay and then we write h of z to be z minus z0 times g of z to the power of 1 by m, okay and mind you g does not vanish on this disc and therefore there is a there is an analytic branch of the mth root of g, okay. In fact there are m of them and you choose one of them and then you call that as h, alright and then you see that if you write it like this f of z minus f of z0 becomes h of z to the power of m, okay and so what you do is that you first go by h then you z0 goes to the origin because h of z0 is 0, alright. So it z0 goes to the origin and the image of this disc is going to be well you know something that looks like a disc conformally so you know I am drawing something like this, okay but I am taking a I am taking a small enough disc there and well and from here to here I make one more I apply another function which is zeta going to zeta power m which is eta, okay and you know this will go to this will take the disc center of the origin to the same disc center of the origin except that probably the radius of the disc will get you know diminished or enlarged depending on what the radius here is, alright whether this radius here is less than 1 or greater than 1 but in any case it will go to a disc center of the origin and now this function is a function that we know very well this is the power function z going to z power m of course mind you m is greater than 1 I am at a critical point, alright m is greater than 1 and you know that how you know that we have studied this already and then to get from here to here so if you come all the way from up to here it is h and then now here it becomes h power m but h power m is f of z-w0, alright so to get f of z I just have to add w0 to it so the transformation is eta going to eta plus w0 that is a transformation is just a translation, okay so this disc will get translated to this, okay so the and well if you look at this picture now it is clear that if I so you know there are m branches of so if I take the inverse functions here the inverse function will be w going to w-w0 that will be the inverse function here, alright and which is of course eta, okay and here the inverse function will be eta going to eta to the 1 by m, okay which has several branches it has m branches, okay and then of course from here to here there is a unique inverse function and that is just h inverse, okay the derivative of h does not vanish you can check that derivative of h does not vanish and so h inverse comes because of the injectivity of h and the inverse function theorem. So you know if I compose all the way here the inverse function is unique here the inverse function is unique because it is a translation it is an isomorphism this is also a holomorphic isomorphism because it is injective so here the inverse is here the inverse is unique and here also the inverse is unique the inverse is not unique in this in here because there are m branches and each of this branches if you follow it with this forward function will get the identity here, okay.  So in this disk minus this portion of the negative with the portion of the negative real axis removed each of these functions eta going to eta to the 1 by m are analytic therefore if I compose it what it will tell you is that you know if I take the corresponding slit disk here centered at w0 then the resulting functions will be analytic, okay so you know I will get functions like this these functions are going to be Zj of they are the Zj's of w, okay and they satisfy the property that this followed by this is the identity here, okay Fj, Fj, F of Zj of w is equal to w for j is equal to 1, 2, etc up to m where the Zj's are the for so what are the Zj's I mean if you start with the value w here, okay then this value w is assumed by F at m points counted with multiplicities and it is those m points which are called as Z1, W, Z2, W and so on up to Zj, W up to Zm, W, okay. So you know this so the you get points here m points counted with multiplicities and these points are the Zj of w and they depend they will change as w changes so for every point here you get m points here which go to that point so this function F is a m is to 1 mapping or outside Z0 of course Z0 goes to W0, okay and no other point goes to W0 but the point is Z0 goes to W0 with multiplicity m, okay because that is what it means to say that Z0 is a 0 of order m of Fz-0, okay F assumes a value W0 which is F of Z0 with a multiplicity m, okay. So these so for any w here you get m values of Z, okay and these values of Z are such that when you plug them back in F you will get back the w, okay. So in other words these are solutions of W equal to F of Z, you are solving from the equation W equal to F of Z you are solving for Z, okay. So you must think of this as these are inverses of F, inverses in the functional sense, okay that is the reason I put a bracket to the minus 1 on top because strictly speaking F is a many to one function it does not make sense to talk about a set theoretic inverse but these are functional inverses, alright just like you know it is the same idea for example when you have the exponential function the inverse functions are the log functions but the exponential function is not 1 to 1 it is many to 1, okay but then we but log is functionally an inverse to the exponential because it undoes the act of it the exponential function. Similarly when you take the mth root function the mth root function is the functional inverse of the function which takes everything to the power m, okay a function which take everything to the power m is not a 1 to 1 function it is a m to 1 function again except at the origin, alright. So but to undo the operation of taking something to the power m you have to take the mth root, okay. So functionally it is an inverse taking variable to the power of 1 by m is a functional inverse and how many such inverses are there are m such, okay. So in the same way if you take any analytic function if you look at neighbourhood of the critical point what happens is that this analytic function has functional inverse there are m of them, okay and each one of them is actually analytic on a slit disc, alright but if you want to actually see them as globally as an analytic function one has to go to the Riemann surface of this f inverse, okay. So you know what happens is that we have we can construct an m sheet at covering so I will draw it like this and so on. So there is an m sheet at covering with a projection and a projection here such that on this you really have a function which I can call as f inverse and again there you see you should understand this f inverse is only a one sided inverse in the sense that you know this followed by f is identity I should say this no in fact I should say this f inverse is a functional inverse which on every sheet assumes the corresponding value fj but the only what is the advantage of this f inverse, okay maybe I will even put a bracket here so that you know you do not get confused but the point I want to say is that this f this the good thing about this when compared to these guys is that these guys are only analytic on a slit domain, okay but the fellow above is analytic on the whole Riemann surface this is the this guy here is the Riemann surface for f inverse the functional inverse, okay and we have seen this already for the case of f the exponential function in which case we got the Riemann surface of the log function which is the functional inverse of the exponential function and also we have seen the Riemann surface for z to the 1 by m which is a functional inverse for f of z equal to z power m, okay we have seen two cases but more generally here is the point is that when you look at the when you look at the exponential function you see the derivative of exponential function is again itself and you know the exponential function never takes the value 0 therefore it is derivative never vanishes, alright so somehow there since the derivative never vanishes it is locally 1 to 1, alright therefore it was easy to write the inverse function itself which is a which is given by a branch of the logarithm, okay but the point because the exponential function has no critical values, alright whereas we are now in a bad situation you are what you are saying is take a function which unlike the exponential function has critical values how even if you take a critical value in the deleted neighborhood of the critical value this function also admits functional inverses the functional inverses they all can be put together as a single analytic function on a Riemann surface, okay and they are they give the solutions for the independent variable in terms of the determinant variable. So they solve z for w, okay you get z as a function of w, okay so let me write this down so the point I want to make is that the functions zj of w are analytic in the slit disc w0-delta w0 yeah I should this is what I should throw out so it is mod w-w0 less than delta-you throw out the portion parallel to the negative real axis from the to the left of and including the center w0 so it is going to be w0-delta w0 so this is the line segment from w0-delta to w0 with the right end point w0 included and the left end point w0-delta not included this is what you are throwing out from this disc to make it a slit disc and on this slit disc each of these functions are analytic, okay and of course you know but all of them glue together to give a global analytic function, global single valued analytic function f to the minus 1 on the Riemann surface for f to the minus 1, okay and the Riemann surface is you know is obtained by pasting carefully the upper you have to take m copies of this disc the slit disc, okay but do not throw out you take the cut disc not the slit disc, okay which means you do not throw out in the slit disc you throw out the this piece but now you do not throw it out you just cut it and you do a cut and pasting process where the portions above the line segment in one disc are joined to the line segment and the portion below in another disc and you do this repetitively, okay and then the last disc you pasted with the first one, okay this is something that is very hard to visualize in three space, okay but then you can do this and you get a surface Riemann surface that is the Riemann surface on that Riemann surface this you get a function which is on each piece that you have pasted equal to the corresponding Zj so on the first piece it will be Z1 and as you move to the second piece which has been pasted to the first piece the function becomes Z2 then as you move to the third piece it becomes Z3 and so on, okay and of course the last piece is connected to the first one, alright.  So it is nice to see that you are able to even at a critical point you are able to get inverse functions that is the whole that is the, that is the beautiful thing that you have to notice, okay even at a critical point you are able to get inverse functions functional inverses for your function you are able to get, okay. Now what I want to say is that I want to say more I want to actually say that these functions are actually solutions of a polynomial equation, okay the solutions of a polynomial equation whose coefficients are analytic functions, okay and it is a that is a very deep fact and so let me explain that, so let me do the following thing consider the functions the symmetric functions functions in the Zjw, okay consider this, so you know if you give me a set of functions then for example if you give me a set of variables then you know how to construct the symmetric polynomials in those variables, okay namely what you do is you the first symmetric polynomial is simply the sum of the variables. The second symmetric polynomial is a sum of variables taken two at a time, okay and then the third symmetric polynomial is sum of variables, sum of products of variables taken three at a time, okay the second symmetric polynomial is sum of products taken two at a time and similarly the jth symmetric polynomial is you take a product of the j variables and take all possible such products and take sum, okay and of course in this when I say product the product you do not worry about the order, okay the variables are assumed to commute, right. So in the same way if you give me any set of functions I can construct symmetric functions from the given set of functions by looking at the corresponding I use the same method, I use the same definitions that I use to construct symmetric polynomials in a given set of variables only now that I am thinking of the functions as variables. So what will be S1, S1 of Z1, S1 of Z1, W etc. Zmw the first symmetric polynomial will be just the sum of the ziw or zjw, okay of course j equal to 1 to m. So the first symmetric polynomial in m variables is simply the sum of the variables, alright. The second symmetric polynomial in this will be now you have to take sum of products of variables to a time. So it will be in the form sigma zj1w zj2w where j1 is strictly less than j2, okay this is second symmetric polynomial and so on you can define the earth symmetric polynomial which is now you take the sum of r of them, sum of the products of r of them so which means that you write zj1w into zj2w and so on you go on up to zjrw you take r of them take the product and then you take the summation over all possible uhh such uhh r indices, okay and if you go on like this the last one you will get is the mth symmetric polynomial which will simply be the this should be the sum of products taken m at a time but there is only one product taken m at a time because there are only m of them so this will be only a single uhh expression not a sum of expressions it will be a single product this will be just product of it will be just the product of all the zj of m over j, okay. So you get these are the m symmetric polynomials in all the zj's, okay and what is the property of the symmetric polynomial this property of the symmetric polynomial is that property of a symmetric polynomial in these m variables is that if you change the variables by permutation the value of the polynomial does not change, okay. So that is what symmetric polynomial means, okay it is invariant under the action of the symmetric group, alright for every sigma in Sn so S so you know I will okay. So let me use uhh let me use let me use small s because it is better so that I can use capital S to denote the symmetric group okay which is just set of group of permutations permutations of n symbols m symbols it is a set of all bijective maps uhh from a set of m elements back to itself okay it is a group under composition is a symmetric group and you and the point is that Sr of uhh if you take sigma x1 etc sigma xm is the same as Sr x1 etc xn, okay. You apply the value of the symmetric polynomial does not change if you substitute for a variable for the variables a permutation of the variables and that is the reason it is called symmetric polynomial, okay and find and what is the advantage of looking at the symmetric polynomials you see the way I have defined them these are also functions of W, okay these are also functions of W and of course they are all they are all built by taking products and then taking sums so all these fellows they will all be certainly analytic functions on the they will all be analytic functions on the slit disk but the big deal is that they are not only analytic functions on the slit disk they are actually analytic functions on the whole disk that is the amazing thing, okay. So the so here is a fact all each or each Sr of z1w etc zmw is analytic in the whole disk this is the this is the amazing fact, okay and so let us let us grant this fact for the moment then what does it say it says that it says the following thing. So consider the polynomial z-z1m z1w into z-z2w and so on z-zmw consider this polynomial this is a polynomial of degree m, okay whose roots are these m functions I mean whose zeros are these m functions this polynomial becomes 0 whenever z is one of the zi's, okay. So the zi's are roots of this polynomial, alright of this zeros of this polynomial, alright but then if you expand it out the questions will come out to be as you would have seen in any course in algebra the symmetric functions up to a sign, alright. So what you will get is this will become z power m plus minus 1 to the power of m minus 1 s s1 of z1 of w etc zmw plus minus 1 to the power of m minus 2 s2 of z1 of w and so on zm of w and so on it will end with the constant term which will be it is going to be minus I have to worry about my my signs in this case is going to be I choose I think let me adjust the signs this is going to be finally I take minus 1 to the power of m sm of z1w and so on zmw only things I will have to take the sign for example and I have to add the questions also say here I want z to the m minus 1 so which means I how do I get the question of z to the m minus 1 I take I choose m minus 1 of these to be just z and the remaining one I choose it to be minus of certain zjw and then add it.  Now so what did I just say I said that you see the ziw are zeros of this polynomial but what is this polynomial it is the same as this polynomial but what are the coefficients now the coefficients are s1 s2 etc sm up to sin but what I say about s1 s2 etc up to sm they are all analytic functions so the m these m functional inverses for f are actually zeros of a polynomial with coefficients which are actually analytic on the disk on the target disk that is a fact that I want to say ok so and it is thus the solutions to z for w equal to f of z are zeros of a polynomial with analytic coefficients this is the fact this is a algebraic fact ok it is an algebraic fact it says that you have you have found you have found bunch of functions which are which are zeros of a polynomial with analytic coefficients ok and in fact this is of great significance in Raymond surface theory alright probably at some point later at some later point of this course I will try to explain that but now for so you know so the moral of the story is that all these functional inverses are zeros of a nice polynomial ok the only the only fact that needs to be checked is that each of these is analytic alright now to prove that it is analytic there are let me at least first try to begin by convincing you that they are at least continuous leave alone analyticity see the problem is you know if you go back these functions they will you know if you if instead of throwing out this this ray ok if you keep it but you cut the portion of the disk on the ray and below it and separate it from the portion of the disk above it then on that they will become continuous they will become continuous it is just like the log function you take a branch of the logarithm the branch of the logarithm if you take the principle branch of the logarithm for which the imaginary part is a principle argument which varies from values starting from minus pi and going all the way up to values strictly less than plus pi if you take that as a function the principle branch of the logarithm then you know the real part is always continuous because it is the natural logarithm of the modulus of the complex number which is which is a continuous function the problem is only the imaginary part which is argument and what is the problem the problem is that you know if for all points on the negative real axis and below the negative real axis the principle argument is you know is greater than or equal to minus pi ok whereas for a point just above it above the negative real axis the argument is close to plus pi and lesser than plus pi so there is a jump of almost 2 pi on the negative real axis and therefore you have discontinuity on the at every point on the negative real axis. So suppose I separate the points of the points of the negative real axis above the points of the plane above the negative real axis from the negative real axis and the points below ok by separating it I am saying that you know the points above the negative real axis are not close to the points on the negative real axis and the points below that is what this cutting means ok and when points are not close I do not worry about continuity, continuity I worry about only when points are close ok so once I cut it if I try to check continuity at a point on the negative real axis I am only going to check in a neighbourhood in a disk half disk which lies in the negative real axis and below it I am not going to worry about points in the half disk that lies above it alright. So you know if I cut this instead of deleting it if I cut it ok then these fellows are going to be continuous ok but then what happens as you go across the negative real across this line segment if you go from below to above what happens is that the zj the values of zj will change from zj to zj plus 1 ok depending on whatever you are ordering is either they will go from zj to zj plus 1 or zj to zj minus 1 depending on the way you wrote it ok and that is because the function itself changes and what you do is you cut and paste these various copies m copies of this of this cut domains not the slit domains the cut domains to produce this remain on surface in such a way that as you cross the this ray on one piece ok the function zj changes to zj plus 1 which is the function on the next piece ok and that is reason why all these functions agree and they become a continuous function on top ok. So the moral of the story is that as you the problem is with the problem is with points on this ray for each of these functions ok what is the problem as you move across that ray the zj will become some other zj plus 1 or zj minus 1 alright but if you look at the symmetric functions ok and you do the same business you see a symmetric functions will not be affected ok for example you know if I take the sum of all the zj's and if I take if I take the w and move it across if I move it across this ray ok that I if I move it across this ray what will happen is each zj will be replaced by the corresponding zj plus 1 ok each zj will become the corresponding zj plus 1 ok and but then the sum will remain the same ok. So what I will get is instead of getting z so you know if I start with so let me if you want let me even draw it so that you understand what is going on so here is my ray this is my w not and you know suppose I start with the w here w1 and I move across this ray and go to w2 ok then what will happen is that you know zj limit w tends to so I will put keep this as w and let me call this as w prime w tends to w prime of zj of w what you will get is you will get zj plus 1 of w you will get this this is what will happen ok or you know it may be zj minus 1 of w prime depending on how you rotate alright this is what you will get but it will always be plus 1 or always be minus 1 depending on how you rotate. So what happens is so you know if I take limit w tends to w prime of for example the first symmetric polynomial of z1w etc so on zmw what I will get is I will get it back I will simply get I will get the first symmetric polynomial evaluated at if I of course the symmetric polynomial is a polynomial in the variables so it is continuous in the variables so I can push the limit inside and apply the limit to each of the variables ok and if I do that I will get well I will get z2w and so on and you know and the point is that zmw will go to z1 because it is cyclic alright. So it will go on at some point I will get zmw and then I will get zm plus 1w or I will get the other way round the index may come down it may be zmw z1w and so on zm minus 1w this is what I will get but both these are the same as this in any case both are equal to s1 of z1w and so on zmw they are the same because after all the s1 is supposed to just add all of them and whether I add from z2 to zm plus 1 including zm or zm to z1 to zm minus 1 and then zm I am going to get the same result ok. So what this demonstration tells you is that the value of s1 of the first symmetric function of these m functions that value does not change ok. So it means that this first symmetric function is a continuous function of w and of course you know I will have to put I have to put w prime since there is a here these are all primes these are all primes and so these are also primes ok these are primes. So the moral of the story is the symmetric function will not be affected and I have written it down for the first symmetric function but you know for all the symmetric functions this is going to happen ok what is going to happen is when you when you cross the troublesome ray ok the symmetric functions are only going to be permuted by a permutation which is given by shift in the index alright and but when you make a permutation the symmetric function is not going to change the value of the symmetric function is not going to change because it is even in terms of permutations therefore what is going to happen is each of these si's each of these sr's they are all going to be continuous even on the even on this even on this ray ok and therefore you can now believe it is very clear that each sr is therefore certainly continuous on this on this disc ok. The only issue is now that is left to be fixed is that it is actually analytic ok and the fact that it is analytic can be for example seen by what is called the principle of analytic continuation ok which is what I am going to discuss in the forthcoming lectures ok. So I am going to next go on to discuss analytic continuation and the so called monodermy theorem alright and it will follow from that discussion that each sr is not only continuous as we demonstrated it is actually even analytic ok so with that I will stop now.