Welcome to this special webinar virtual round table we are so used to it now though the real world is also opening. This special virtual round table is in partnership with Tabula brought to you by Exchange for Media in association with Tabula. And the focus today is the consumer durable category. And the way it has changed over the last almost close to two years. Also the discussion is important because we are at the start of the festive season. And which means that a lot of consumer activity will be witnessed but it's with a change mindset. The behavior has changed the way consumer interact with brands has changed. These are the some of the key discussion points that we will have in the course over the next one hour. And I might also add that today we have some of the most imminent marketing leaders with us. I want to introduce them. We have Mr. Amit Tiwari. Mr. Amit Sethia, CM of Cisco, Mr. Adil Sanwari, head digital media and transformation Sri Lanka and Bangladesh, HP India. Mr. Bharat Arora, a country manager, India Tabula and Mr. Prashan Dal, marketing director, AO Smith India.  And thank you so much for taking our time. I want to come to you first, Mr. Sethia, straight away diving into my first question. You know, we are at the, as I mentioned, getting into a festive mood, but in a very changed circumstances. The setting is very different. The sentiment is very different in this kind of a setup in your view. How can brands make the most of the key promotional period? Is there other set rules that brands need to follow to make it more effective in the context that we are in? Thanks for the question. And I'm so glad that I'm a part of this discussion today because I can see a lot of synergy getting created. And because of the fact that it's a consumer durable category. So, coming back to your question, it's very imperative that the moment you think of the promotional period or the festive season, you're bound to think about discounts, sale, et cetera. I think that is what comes to our mind and more so as an Indian customer. But I think personally the way I have seen this entire quotient sort of coming down over these last couple of years is tremendous. Let us look back, say around 10 years or so. We used to have these discount based events maybe twice or twice in a year, right? Not beyond that. We used to go to a regular retail market or the mall also and we used to talk about that. That was the conversation that people used to plan in advance that we are going to buy these items, et cetera. During this specific time and festival when you used to get discount and discount was not very across the year, which actually became a phenomenon later on. Not today if you go to any mall, you'll find that discount banner always hanging next to the main gate. The only thing that changes is the percentage, right? So I think over a period of time that discount as a word or as a proposition, I think personally has lost its sheen right now. You can even talk about e-commerce right now. I know there are these big events that happen, the BBTs of the world, wherein you get amazing discounts. But look at the way the customer approaches that space. He will look at as to what product he wants to buy and from which brand he should be looking at that product. Obviously, this is the review, the rating, the preference, et cetera. And then he will go and buy that product and maybe whatever discount he will get, he's happy with that because ultimately he's buying that brand. So I think over a period of time, I don't believe now discount or anything which is close to this proposition is kind of a guarantee to make the most out of your promotional period. If you look at the example of this brand, SESCA, my narrative is always brand led when I go out and talk because we have been talking about the warranty, the power saving, or the usage life of the product, et cetera. But we have never spoken about a specific product or egg-pake, free-lay-low types, et cetera. So I think that's where I'm coming from that if you really want to make the most out of your promotional period, it is very important for a brand to really figure out and check as to what you're doing, otherwise in the not so promotional period. Right. Mr. Tiwari, to you, being representing a very broad, being the marketing leader in the space, tell me, we know that digital age consumers make the decisions in a certain different way than it used to be. How can brand overall maximize the promotional period in this changed circumstance? Thanks, thanks, Roil, and good evening, everyone. I think the larger piece Roil, which you mentioned, which I might also somehow try to cover about. I see in the last two years, and I think last two festivals season last year and this year, the entire consumer purchase pattern has changed big time. The decisions have changed big time. It is nothing to do with what is available and where it is available. It most important is what I want and what is the period which I really want. And it can be whatever the platform, previously you won't believe it, you haven't seen that big ticket items which are costing 50,000, 60,000, 70,000 can be bought online today. Irrespective today whether I have a discount or discount, but I need something on that particular requirement, I can buy it where it is available for me and it can give me a delivery which is much better. There are products in which many categories require installation. People are coming out with different ideas where you can actually do it yourself without even using any particular external interference to build it. So more importantly, it's not about where you are actually selling, what is the promotional period? It's about what is the change of the entire pattern of consumption from a consumer standpoint, are you able to match or are brands able to match that entire thing? A digital is no more a medium, it's a party play. So it is not about whether you advertise or you don't advertise today, your life evolves around digital.  How do you do it is most important and how do you reach that narrative of the consumer that that's very critical in the entire journey. Thank you. Very well said. Mr. Anwari, I want to dump you at this point. In your view, are there any set of rules that brands can make it more connected with, feel more connected with consumers and have the maximum of the promotional period? How is your brand looking at this? What are you personally doing to enable this? Thanks, sorry. Sorry, is that a question for me? Yes, Mr. Anwari, sorry. Thanks, Roy. Hello everybody. You know, it's a, when I think about the festival time, especially in India, you know, it's mostly about togetherness, it's mostly about celebration, it's mostly about being with your family, right? I think where we've hit the chord right is about creating that kind of a communication, which makes the consumer believe that what we're trying to do as a brand is bring them all closer, right? We're trying to make that bond stronger. I'm sure that all of you must have seen our Diwali ads in the past couple of years that we've been doing, right? They've created that kind of an impact that everybody today is expecting HB to bring out, you know, the better version of a last Diwali campaign that we did, right? So our objective is very clear. See, we today, especially in our category, right? I mean, we live in a world where we don't need to tell too much to the audience or the customer about what the product is all about. You know, they do their own research. They have multiple platforms today on the web where they can research about the product, know more about the product. There's a tons and tons of video and reviews that goes on that the customers can figure out what to buy, right? So the responsibility from a brand's point of view is to how do I make sure that, you know, two ways to look at it, people who are the switchers. And I know for a fact that every year over 50% of your, you know, category customers are switchers, right? I mean, today they have HP, tomorrow they might be with some other competition, right? And similarly, there's a set of brand loyalists that I need to take care of, right? So in my view, the tactics that we apply is we look at the data overall and the baby bifurcators between brand switchers and brand loyalists, right? Brand switchers, of course, because it's festive time, everybody is coming to get a good deal. You know, make them feel special, make them feel, you know, that this brand is worth that. Maybe, I don't know whether discounting is the right word or whether giving them something additional is the right word. Number one is that, number two, from a brand loyalist perspective, this is the time to make them feel special in terms of giving them something exclusive, right? Customizing things for them. So I think from HP's point of view, these are the two three things that, and again, you know, sorry to say, but there is no rule to it. There is no silver bullet that will, you know, sort of assure success for you as a brand, but it is always going to be a hit and trial method. We all learn as we do and sort of move forward with one activity or the other, right? So I think the best way to do is create that bonding between you and the customer because I don't have a dearth of awareness today for the brand. What I need to do is to engage my audience in a way that they know this brand is still cares for me, has something exclusive for me and will do something special for me year after year, right? So I would say that's our brand sort of thing. Lovely. Mr. Dara, your thoughts on this? So I would tend to agree with Mr. Sanwari, but I would just like to keep a table across a couple of perspectives. One is that how, you know, the emergence of e-commerce platform has affected the appliances industry. I think it is now, if you look at the last couple of years, the contribution to the business of e-commerce as a platform has just doubled. So I think the kind of focus in the marketing mix that you have on e-commerce has gone up by leaps and bounds. So things like, you know, Great Indian Festival and the big billion days are definitely revenue earners for you. So here the challenge for the brands is basically how to connect with the customers along with the value proposition that you are giving. That value proposition can be in terms of price, it can be in terms of the service that you're offering. It can also be in terms of how much, you know, affordability you are promoting in terms of some of your key product lines. So as a brand, you need to be very focused in terms of what are you planning for these big festivals, which are now contributing to a major part of your total revenue. You need to obviously match your content with the intention of the consumer. So basically matching content with intent has to be the key. There are things like, you know, exchange offers, no-cost EMIs, one-day service, et cetera, which are big drivers on these platforms these days. So that's very important. Also, you need to understand how much efficiently you are planning the media. And it will be very important to monitor the performance of your conversions on these platforms on a daily basis because the things, the bids keep on changing by the hour on these platforms. So it's very important to monitor and get the correct ROI for your brand. So that is, I think, very important. Of course, I mean, the overall, you know, as I was telling you that you need to understand how to match the creatives or the content to the intention of the consumer at what stage of purchase journey he is. So address each of his, you know, journey with a creative, which basically translates into a storytelling and aids him to finally, from an, you know, kind of an awareness interest to a conversion, to an awareness stage to a conversion stage. So it's, and also with all the advertising monies shifting into digital these days. It's very important to, you know, have a very seamless kind of an integration between your offline strategy on media, mixing with the online strategy on digital. So basically, they have to be complementary in nature. So the word is be agile, be watchful and deliver the optimum ROI. Right. And the way consumer sentiment has got affected, I think they want definitely more value out of the purchase, you know, I think brands cannot, you know, brands have to take that in view. I want to come to you, Mr. Aurora, at this point, you know, you bring in a different perspective than the other panelists here. What is your observation given how brands can get the maximum out of this promotion period? I think what I have actually completely agree with what some wallets have said, Adil was perfectly all right saying that, you know, the market is moving toward people are already aware. So it is very, very important for yourself to make sure that you build us, you know, such a kind of a connect or a bond with your customers so that, you know, they, it's more of a pull strategy that we should to cross. Of course, during the challenging period, everything was getting involved, consumer behavior was changing. It was very, very important for all the brands coming from outside. For example, Tabula is one of a very reported performance platform where, you know, brands come to us just to make sure that they build their from middle funnel to the bottom of the funnel. And we see huge changes coming up where everything was changing from what Prashant Mr. Dhar was saying about the creative side. People were talking, trying to talk to the customers, impacted with them in terms of the hard times, but talking in their language. So every creative that was playing at Tabula was very, very much bonded, much connected, talking about not only selling but it was telling a story, story which connect with them. What Mr. Sanwari was talking about, building the connect. So that was actually coming through the entire funnel where people were trying to build some of the awareness, asking about people's health, but eventually trying to talk to them, build bond, asking about their wellness and then suddenly, possibly, you know, tell them that, you know, this is the place that possibly that can help you do, this is the place you can buy what Mr. Thivari was also trying to touch about that. It is not about where and what you want to, you know, buy it. We saw, specifically at Tabula perspective, we saw, you know, consumers were making purchases we never saw before. Okay, so in terms of the bottom line, for example, talking about the consumer electronics or consumer deliverable as a vertical, which we saw, people were buying first time online, which we never imagined. So of course, because our KPIs, given to us was changed from visits campaign, everything was talking about CPA, because it was business survival. And we saw that, you know, how various brands come over and talking about various acquisition strategies. And we saw what Mr. Thivari, beautiful design, said that this is, even if somebody is like 2 lakh rupees INR and they were okay to buy at this point of time. So that was very different consumer behavior. So very impressive to see. Right. You know, I mean, there was a point mentioned that today, the brands alone don't do their work to reach out to consumers. The consumers do a lot of research, you know, especially in these times before they make any purchase. And we have often asked this question that what are the learnings? What are the learnings from the last two years?  Mr. Sethi is starting with you again. Talking about the learnings again, you know, because we had sort of learnings and the second wave game, there was a different learning, there was a different pivot towards a different strategy. What are the overall learnings as we enter a festival season? Because this is the second time in the last pandemic started that we are close to this. What is the kind of enrichment in terms of learnings that you're going with, with your brand and your promotion? So, I will point out quickly some of the key learnings that we as a brand, I would say, and not as a market here, right? Because at a brand level, there is so much that you discover and learn, I think. So first and foremost was the fact that, you know, see, consumer durable still largely is a distribution driven sort of a business, right? And I think that's where we realize that we need to optimize, you know, this particular distribution, you know, aspect of the brand. So I remember during the first lockdown, the Government of India actually announced, say, example, you know, the grooming appliances as, you know, the semi-essentials for the consumers. And that is when we actually optimize the distribution channel for this very category and ensure that the products are placed across all the medical shops in the country because it was the only medical shop along with the Kirana shop that was actually open for the Indian consumers.  So the usage of this very product, which was always looked at from the illumination perspective went beyond that and actually was used in the space of disinfection actually because suddenly people were very, you know, worried about as to how they can take care of certain smaller items to disinfect on day to day basis. So we were using these kind of specific LED UV products. I remember marketing was in such a tight spot because of the fact that, you know, these, you know, special treatments to the content that we give was always, you know, felt to be very important, right. But suddenly we realized that, you know, we don't have access to these kind of studio treatments. So suddenly we realized that, you know, we were churning out the content without those, you know, final glossy treatments. And still it was, you know, clicking with the right audiences, right, because the content was very authentic. So I think this was also one of the learning that we realized. Apart from that, yes, I think the demand for the smart home products sold to new heights because of the work from home culture. People very, very much open about this new, you know, portfolio. You know, and they were also interested to look at as to how they can convert their existing whiteboards or consumer durables into at least, if not full smart, at least to semi smart, right. So all these solutions were tackled beautifully during these last couple of 18 months or so I would say and yes, we also entered a very new category because of the smart watch I would say with a very disruptive price, because suddenly everybody was talking about their health and fitness levels, right. So I think these are, you know, some of the key learnings that we, you know, witnessed over these last, you know, couple of months put together, which is amazing actually as a brand. Right. Not just as a brand but as a marketer, what are the big learnings for you and what are the new insights that you gather. So I think first thing, whatever is every marketer instance, we're talking the marketing as a fraternity, and when I talked to a lot of my marketers in last 20 months what has happened is whatever we have learned for the 20 years that needs to be rebooted, all the systems of marketing need to be rebooted. So that theories and principles was fine. But everything has changed. And what has happened to this rebooting that you need to start relearning new rules and new rules of the game. And what has become the three main rules of the game is three T's trust transparency and technology. You any brand that you actually operate you need to have a trust which is a very, very highest order. Otherwise you will not be able to build any particular substantial gain in any of the things that has to be absolute transparency that you need to build across the entire spectrum because consumer is far, far more important and is more sensitive towards any brand engagement that it's to technology has become a part and parcel of everyone's life. You see today technology transformation people are talking about for last many years but the way it is technology transfers happen for a four year old till 80 year old the transformation has been absolutely, absolutely high in every part. And that is how it actually defined and redefined the rules of the game. If you're up in all the three T's that are actually talking about which is trust transparency technology, you are much ahead of the game and your brand is much more visible in terms of what we need to do. If you're lacking in any of the things you will definitely find a huge impact in the outcome, whether it in terms of your brand response or in terms of your brand sales that will be reflected. So that is how the rules have actually changed and the traditional principles just remain as a principle because you need to start building and rebooting yourself in a bigger fashion. Trust transparency technology very well put Mr. Kewari, thanks for sharing. Mr. Sanwari, how about you? How would you define your learning? We were not prepared for this, none of us were prepared for this, right? So saying that we already have certain weapons in our arsenal is, I don't know, it's the wrong way to put it across, right? I think the best learning that we've had is how important it is to be agile, how important it is to be extremely flexible, especially in our category, right? When we're talking about a cycle where we know that the person who's bought a laptop would think about buying another laptop in the next five years, right? And so is the case with printers largely, right? So all of a sudden people stop going to office, all of a sudden people, children stop going to school, right? And earlier what used to happen is with a parent, you know, a kid at the age of 8 to 14 typically, you would have, whenever that your father or mother's coming back from office, you would have a spare laptop and then the kid would do anything on the laptop that he or she wants to do, right? With school projects or whatever for that matter. Now all of a sudden everybody needs a laptop because everybody's working from home and so are the schools that are running from home, right? So the way we sort of identified the problem that, hey, you know, there is a problem of people not having an extra laptop or a printer. And there's also an opportunity here where we can sort of make sure that we're not trying to oversell the product by saying, hey, you know what? Just because you're sitting home, why don't you buy another laptop, whether you need it or you don't need it, right? What we did is we sort of, we initiated another way of looking at this entire category by saying this particular product is to do with learning, right? So if I would say we sort of started this category altogether from a learning perspective, I said, if this one laptop, which is typically going to help your kid to do all the school projects or homework projects that's been given by the school, right? And you don't need your parents' laptop. We know that you can't use that laptop. Similarly, we bundled that kind of a thing where we said one laptop and one printer is going to fulfill your needs from a kid's perspective where you don't need any spare product to be buying from, right? And we also knew the fact that at the end of the day, we can't fight with the smartphones, right? Everybody has a smartphone. It's very stupid in our part to say, hey, you know what, today we can work on a smartphone and you don't need a laptop for that matter, right? Or you can take a laptop plus a smartphone as well, right? So I think we were not talking about smartphones. You said you have your smartphone. You can do multiple things on your smartphone. That's great. But this as a package, you know, you need to print stuff. You need to have a physical form of your project and your school project and homework in hand to figure out and do things on your own, right? So these are the learnings I would probably say that helped us create this kind of an opportunity within the market. Number one, number two is from an offline store perspective. And I think somebody mentioned initially about how challenging these times were where you would try and create a lot of footballs to the stores. But unfortunately, that can't happen because all the stores are shut, right? So as a category, we were still falling behind in terms of the customer wanting to take the demo of the product. I guess definitely times are changing and people are moving towards buying this category on e-commerce models. But today also when, you know, people come on the store, the first thing they do is they do the research from across the globe and then they want to come and do the touch and feel of the product, right? So we initiated things like video demos, right, with our ISPs or in-store promoters, right? So these were the facilities that were not earlier available, right? We created, we supported more and more offline stores to create home delivery kind of systems, right? So home deliveries and home demos were something which really helped us as a brand to connect back to our consumer and say, hey, you know what? We know you can't come to us, but allow us to come to you. And of course, these are times I'm talking about when the government had sort of opened up these restrictions of, you know, doing deliveries or reaching out to any individuals out, right? So I think these were the two biggest learnings as a brand that we had and, you know, we acted upon it. And I think fortunately we were sort of able to, you know, create some success out of that. Great. Listen, sir, coming to you and understanding the changes in your category and the way your consumers have changed and your brand approach has changed. Give us a sense of the learnings that you have gathered. Yeah, sure. So there are, I will segment my answers in two parts. One is that about the geography, right? And then the second is on the consumption pattern. So if you look at the geography, so there has been a reverse migration trend in the tier two and the tier three towns. So the kind of growths that we were witnessing in tier two and tier three has kind of doubled over the last, you know, couple of years. And that's primarily driven more by the reverse migration of the working force, right? So that is one interesting trend that we have seen. And it will also, it is also interesting to know that the ASP difference between the tier one and the tier two and tier three towns is not much. So the high value products are still are definitely being preferred also in tier two and tier three towns. So that's an interesting trend that we could observe. The second one is in terms of the consumption pattern and here I would like to mention three key points. A couple of them was also mentioned by Mr. Satya. So one is a very high focus on health and hygiene and since we are operating in this space and with water eaters and water purifiers category, we have seen a higher traction over there. And there has been a growth in recruitment in the category. So basically the lower price products have been really being lapped up and are showing a higher growth. Say for example, an instant three liters is showing a much higher growth than the storage water purifier. Similarly, we have seen tremendous growth in the UV water purifiers. So that is one trend that I could see. So it is helping in terms of the expansion and the penetration of the category that is one. Secondly, it's about, you know, people generally becoming more environment friendly or environment conscious, and they are also seeking this value in the products that you are offering. Right. So in some of the products that we have launched in the last one year have been directed towards this proposition and have been really appreciated by the consumers. The third part is about the with the increasing work from home comfort and connectivity at home is of paramount importance. So the adoption of connected products are surely getting a boost due to the due to this, due to these last 18 months. I think these are some key broad trends that you know we could decipher in the last 18 months or so. Mr. Arora, you heard all of them and you have dealt with brands. What are the takeaways and observations that you would like to share? Sure, thank you. Actually, it was very interesting journey for us. Plus two years of course was very challenging for every company. We faced something which was never anticipated. We never forecasted that this something happened. The first thing that happened with Tabula that we did is the key that we for us is adaptability. We make sure that we adopt towards the business that we are in. So at Tabula, primarily we have two sides of the businesses. One we have supply side which are publishers and then we have demand side which are advertisers. Since you know we support for open web, it was very imperative for us just to make sure that we support and stand with all our publisher partners. So that was the first thing that we did and thanks to all our partners. We decided to sell together. We decided to be intact and we see how to face it together and build something which can be much more better for the entire media industry. The second side which was demand side which is advertiser side. So at Tabula we went back to basics. So we never spoke about eyeballs, visibility, clutter and clutter. We said everybody, every business is important and for every business to survive, it is important that performance will be the key. So we made sure that we molded ourselves, adopted towards our more of a performance side of the business where we went back to certain important tools that we have. For example, we have something called Tabula newsroom. So that's a beautiful tool that is actually a tool which help all editorial or writers to look at insight which is actionable insights. Possibly tells us what consumer is actually looking at open web, what people are reading across where they're interacting. So for example, what Mr. Sanwari was talking about that people was talking about health fitness, learning. So all these insights, we've got to know that we're in the open web where people are consuming it. Okay, so now we have no lot of data and data insights. This is the same, we made sure that we build certain strategies and then we also had a global initiative called Creative Shops. What Mr. Dharba was talking about the creative that we spoke about before. So what we did is we married to work together. We had a creative shop where we went back to all advertisers told them that this is something that should work for you. This is data insights that we have. This is a strategy and this is how you can build your creative so that you get more performance. So another day, because everything was for us was cost by acquisition cost per lead because everybody was in the survival mode. So that was one thing, you know, that was very, very important for us to make sure the other things, of course, and then things were getting better. So then it was also our task just to make sure that we help make this comeback for all the brands. So then we launched a product called High Impact Placement where we made sure that we give visibility along with performance. So I think the key thing I would say during this point through the learning, we evolved as much more stronger, full-fundal marketing platform. And for us, the key for success was just to make sure to adopt and adopt fast and be together and work like a team. So that not from the supply side, not from the other side, for example, all the key, you know, industry experts sitting here, of course, just to make sure that we work together as industry as a whole and then we make sure that we pull ourselves together. So that is good. And as we speak, we are sitting on cotton, cotton, we're sitting on the best of the quarters ever globally tabula as well as tabula in India.  Thanks to Arora for sharing this insight. You know, what has, what this time has also done is not only changed the consumers, the brand strategy, but also how brands spend and, you know, divide their budget. It has also impacted that. That's my next question to Mr. Satya, that, you know, if we look at the recent times as a brand, how do you optimize and plan the budget allocation across the multiple digital channels? Also, with the same follow up question that, are there any big gaps that you have seen in their offerings and what brands want? So I think the first and the foremost thing here is that, you know, as a marketer, we used to always have this golden allocation, I would say 70, 20, 10. What is this, the person will say, and more than the consumer durable space I'm saying, 70 was always ATL, 20 was VTL and 10 was digital. You know, I think that was the sort of, you know, a conversation till maybe 10 years back, you know, but gradually because of the advent in terms of technology and digital avenues, you know, things started changing. You know, more 70, 20 and 10 for sure. And at the same time, even the allocation within the digital space is extremely dynamic. You know, you will not be saying that okay, fine, this much portion is actually, you know, contributing, say to SEO or content or video or SEM, etc. Because everything is extremely agile. And I think that's where we focus that, you know, more than allocating monies, you need to be very agile in terms of listening to what is happening around you in terms of digital. You know, response. And see, I think everything need not be ROI based I think that is something I strongly believe in because there is so much of performance that in this entire journey, you tend to become transactional because digital space is such I mean like by the very nature of the space, you know, and you don't even realize that you know, you have been getting a lot of money and revenue, but where is the brand standing is, is it, you know, able to, you know, you know, go and put a narrative to the customer. So I think that's where I draw a line personally. And second is, I always try to keep at least a buffer of 5 to 10% of my overall budgets just to do some trial and error and failure. And that is also okay because unless and until you try new channels, new mediums, new avenues, I don't think there is going to be any learning otherwise up with Facebook, Instagram.   Everything is million metric, right? There is nothing below that. Now, I think in today's time, it is so easy to reach that metric in no time. I mean, like, I remember I was in real estate, and I was doing this digital campaigns and we used to actually wait when this golden number will be achieved. So, it happens like this in no time. So I think for me that's it's like an eye wash for me, which I'm very, you know, sort of, you know, a little away from I don't get impressed very easily. I think, apart from that, the only thing I have a small hiccup is the fact that, you know, the kind of solutions are given to me are very, you know, copy based. I mean, like, you know, because it just works out on everybody, I think. So I think there has to be a specific narrative, because I have seen so many partners coming in and the only thing that they change is on that first slide, they will put a Cisco logo.  And the only thing that will change is from Cisco logo to some other logo, right? So I think that's a small problem I have. I think when you are coming and approaching for a partnership, it needs to be like really thought through and very, very relevant, not exactly, you know, driven by only numbers and transactions and million metrics. So that's where my response is. Absolutely. To Mr. Tiwari, I want to come to you here, your thoughts on this. I think what I heard from Amit, I think, see the, and that's what I always for possibly one thing which I agree with him, this, see this definition of ROI is very different from different. And I personally feel as a marketer, it is not about return on investment, it's about return on insights and return on innovation.  It is just a simple mathematical tool that you can actually apply on any exit. I think when it comes to marketing and specifically when you talk about digital marketing and the space that you're talking about, it needs to have the calibration every now and then. What I used to do two weeks back may not be relevant today. What I used to do for an X category may not be relevant for why otherwise there will be only one simple spreadsheet and you don't require so much of detailing and deliberation what you need to look for it. So I think the entire consumer decision journeys have transformed into consumer digital journey and both has to marry together, whether we call it an ROI or whether you call it insights or innovation driven. But the larger pieces in terms of how it is actually matching my objective of reaching the consumer getting the getting that acquisitions at the lowest minimum cost, but the maximum impact that is what I would actually urge on this particular point. The points were raised that how agencies are pitching and with the same copy piece model and how the 70-20-10 thing has changed. Tell me your side of the story, especially when the budget allocation across multiple digital channels, what has changed? I completely agree with Amit when he said the 70-20-10 was a typical ratio that we've all heard in our profession, in this particular profession, especially being a digital marketing right from day one of my profession. I think I used to fight with my bosses, especially with the CMOs. I had to really convince them about why is it so important to put money on digital. So the times have definitely changed. I think we reward as marketeers about digital is not just an alien within the marketing ecosystem. It is equally, you know, an equal brother or sister with an ATL or an ATL as you want to leave it as right. So I think there is no specific logic for us to put X dollars here versus Y dollars there in HP. I think what we try and do is, and I think somebody also mentioned earlier is about what is the objective that you're running after? I think that's for me is the most important part of the journey where I started if I'm looking at awareness as the core KPI or as the core objective, I know that I need to make sure that I reach out to places where number one, I find the right kind of audience. When I say the right kind of audience is definitely somebody who will respond to what I'm trying to say. I'm, I'm, I don't want to sort of beat around in the bush. I don't want to hit the arrow in the dark but I know that, you know, it's just a black hole. The money is going to go somewhere but I don't know what happens at the end of the day, minus the fact that you will definitely get some impressions and so called clicks and visits at the number right. I wish somebody within the industry could run a campaign on cost per quality visit for that matter. I mean, of course, everybody runs a campaign called cost per visit, right? Somebody runs a campaign called cost per quality visit. I would love to run campaigns with that publisher or with that organization, right? So I think as we evolve in terms of understanding the customers, the KPIs that you're running after should also change, right? I mean, you know, it's not about how many views do you get? It's not about how many people do you reach out to? I think those are all input metrics. The more money that you put, the more views or so called impressions that you get for your ads that you're showing, right? So I think interactions, I think, I don't know. I mean, I still, I'm still a sucker for, you know, how many people have actually viewed more than 75% of the video, video ads, what your objective is, right? So I think those are the few things that as an organization perspective, we run after and we call them as fruitful KPIs and objectives and targets being put up with, right? On the other hand, I also understand that it's important somehow, you know, in the country that we live in, where we all talk about, say, and I'll give an example, a classic example of, say, IPL, right? Mine is the brand name and everything that I'm keeping in mind. So you know for a fact that today if you try and leverage yourself on a platform like IPL, right? You have no idea who you're reaching out to because today in India, a kid at the age of 10 years versus a guy at the age of an old man at the age of 60 years, everybody's watching cricket, right? I'm not sure whether and if I'm trying to reach out to an audience segment within 18 to 25, I'm not sure who's watching my app. I'm convinced with the fact that this audience is going to be a part of this overall audience who's watching the game because cricket today is a religion in the country. And if I as a brand, I'm jumping into it, I'm sure the way to look at it is if I'm running after a certain specific KPIs and objectives, I don't think jumping out in the well with everybody is the right way to go about it. You pick your battle, see what you want to do, convince your stakeholders. I think it's one of the most important things to do today as a digital marketer is to convince your stakeholders and tell them what's right and what's wrong because we all, you know, sort of foray from those times where you put money in TV, that is the epitome of success. Today is not the case, I just gave you an example of IPL. You guys will watch IPL, I'm sure. Count the number of ads that you see if you don't have a premium subscription. And you will realize that every brand right from A to Z is part of cricket today because everybody wants to take an advantage. Yes, true. But are you getting your objectives and your KPIs fulfilled? I'm not 100% sure about that. So you will get a lot of accolades within your organization about the MDs of the world telling you that, oh yes, we were present on the biggest media moment today in the country. But at the end of the day, you know how many relevant people were you able to reach out and won those, what those people are going to get you for your campaign. Right, right. Thanks for sharing thoughts. Mr. Dharpreet, give me your side of the story. Yeah, so obviously with the limited budgets during a tough period and with the digital adoption increasing, obviously the shifts in the budget makes are really quite heavily skewed towards the digital communication. So the challenge for brands right now is to how to marry a great storytelling and finally aiding into a conversion. I think that is the challenge that we all are facing as marketers. So storytelling, which means building the brand at the various stages of the consumer digital journey as we call it these days. And how are you aiding that storytelling in terms of getting a conversion and actually acquiring a lead. So that's the, you know, that's the biggest challenge that we are facing and we have to work towards it in terms of, you know, the various touch points that we have digitally as well as offline. So I would not exclude offline from here at all because it's still a very, very important part of the mix. So we have to see that how this, you know, the overall all seamlessness of communication takes place which results in a, in a consumer acquisition. I think that's the that's the biggest challenge and we have to understand very clearly define the objectives that our campaigns are designed for and and and measure those objectives in a very agile manner as I also mentioned earlier on a day to day basis and see what are the, you know, changes that we need to do. So basically it's the creative challenge and the effectiveness challenge I think that's that that is what we are facing right now and that is what we have to address. Right. Mr. Arora to you. When it comes to go to marketing channel. What are brands doing right what are they doing wrong. What is your take on. When we talk about what they're doing right. Basically, because I have serious shift in the change. Okay, people are especially marketer are much more insightful data is something that everybody's looking at, you know, in depth, whatever I am so what Mr. Mori was talking about how our MDs, you know, come back and they're saying this is what is required. But we see the great shift that is, you know, prevailing in terms of the digital marketers. No understand each and every data piece they understand what they would they would like to target. What is the clear objective and what expectations that we have from a specific publisher. So that's the reason you see a shift coming from the ball gardens to open web, where, you know, it is very very clear and evident that the metrics is beyond reach, it is talking about the right targeted audience. There's also talking about right ROI. The ROI could be views, it could be any specific leads slash acquisition, but in terms of awareness in terms in terms of each funnel. So, if I remember when you used to talk about a lot of marketers and brands talking about specific reach is to get what Mr. Amit Sethi was talking about, you know, if you want to have reach one face you can give you XYZ for example I don't know name and publisher generally so one publisher can give you immense reach, but things are much beyond. Right now where people are talking about the full funnel approach they're looking at what right eyeballs visibility that you're getting as per the objective they require what exactly interaction they're getting out of it. That idea of funnel has been dragged properly and the matrices so clear that it is much easier for publisher like us to measure that to go back show that reports and make sure that you know it's like a space where like a win-win for both publisher as well as advertisers. So that's the great shift that we've seen. So at this point I have some audience questions we have around 10 minutes left more than that. I want to take the first question and start with you Mr. Sethi that what factors do you look at before choosing the right marketing tools? What factors do I look at? See, there are a couple of factors that are very crucial for us to you know sort of consider before we decide you know as to which channel we are supposed to swing towards. But more than anything else while we talk about those factors you know it is very important for us and these typically are you know from the digital side actually because you know it gives you so many opportunities to go and create your narratives. So I think that only thing that I look at is is it able to you know grab the attention of the consumer the end consumer that I'm chasing within three seconds or not.  Otherwise there are various other you know objectives that are you know looked at long format short format etc etc which you know side of the funnel with top bottom middle these are the regular ways. My point is the I know for a fact that the attention span is actually coming down drastically. You know there were days when we were talking about 10-15 seconds and today we are talking about 3 seconds I mean like imagine the decrease that has come to us now in terms of timelines. So I think these are couple of things that we look at before we decide on to any marketing channel. Alright, Mr. Wadi there's another question I'll combine the two. So one is the how do brands what are the best ways that brands can choose the right marketing tool and also with the festive season kicking in you know everybody is aggressive on promotion. So there's a lot of noise around a lot of good communication gets lost in this noise. How can brands ensure that they say a float they reach their consumers you know heart despite all the noise around these two questions. First come first is I think Rohin the bigger thing is before you choose a tool choose your objective. Tool will follow but you need to actually decide what the objective is there are empty number of tools that you can even list your entire particular listing of an Excel will finish particular tools will not finish. But what is the my affinity tool that I require for my objective even for one particular organization you may require five or six different tools depending upon what your objective that what happens is most often because tools technology sounds very fancy that adds a lot of which you call as a very glamorous world called mark tech which add a lot of glamour to the entire but your objective is not in terms of selection of the tool. Your objective is in terms of selection of objective that you need to fulfill you are responsible for a function which has to deliver that objective. So select your objective first tool can obviously decide what you need to do. Coming to the second question is yes there will be noise and obviously if you see the number of I don't remember the exact number but in actual calculation it is around close to 47% of the brands that have increased in the festival presence last year on digital as a platform this time it will be much more at least if not more 10% more than what we have last year. How you can actually be is in terms of again getting into the right format that you need to be. And I think I like one of the proposition somebody was talking about and I think Adil was talking about this in terms of you can reach to a number of people but that particular reaches your particular age or you want an affinity to reach for your particular audiences to build. Second thing it's the most important you have to be extremely creative not only from a creative standpoint of delivering a good creative, but you need to be very creative in terms of delivering that good creative. So that people can actually have if you are able to get one particular eyeballs to your creative I think your job is done because you will never get a chance to get a second eyeball because the window is very less. You hardly get a window of around 3540 days to actually exhibit what you need to be. So these are my two bits on these two questions with thank you so much. Thank you, Mr. Diwari, Mr. Diwari quickly to you.  For the marketing tool front I think make data your best friend. As a marketer, I think there is nothing better than, you know, having the tons and tons of data that today you're sitting in that that as an organization you can have the capability or make that infrastructure available for yourself. I think there is a beautiful story that you can create from even one bit of small data point that you have for your customer right I mean that is something that at HP. We try and strengthen ourselves for making sure that we have enough data and whatever data that we get all the decisions that we take is basis that data right so be be your, you know, your sentiments be be the boss campaigns that you've done be be your search trends be be you know your spends for that matter like you will have all that data available for you to utilize and I think. Once you have that the kind of decision making that you can do basis that and it's not about a specific tool or you know about a specific vehicle I think. For that matter if the data tells you to just do email marketing trust me will work for you right so don't be a fashionista. Don't be somebody who likes to it's just about buying a buying a really fancy car, but not investing enough in the driver right so. Why did it I'm sorry I mean spend more in creating that infrastructure that can give you a better result for your campaigns number one number two on the on the storytelling part is what I initially said right. I think at one point in time all of us had this question about long format video and all of us were after running after do a 10 second do a 12 second you know because nobody has time. We are slightly different from that perspective, if the story is good, people will make time right they will definitely that's what we realize in the past couple of campaigns that we've done on Diwali is both those videos were more than three minutes right. We've gotten a great response on so don't worry about what the world tells you in terms of you know, shorter format and this and that. I mean also beautifully said right unless you tried, you will never realize that it's working out for you right so try those long formats work on, you know, a great communication and engaging communication storytelling, and I guarantee you, it will work for you. So I would definitely second what Mr Sanwari was saying and what we need to do very clearly is that we need to have a very powerful creative that is that is definitely there. And that creative should reflect the sentiments that the consumer is right now experiencing and that is that is extremely important and when we are talking about festivities. It has to reflect the overall consumer sentiments so the brand should leverage and be a part of the consumers life rather than you know, giving them some kind of a communication which may or may not be reflecting the sentiments of the consumer so that is, that is definitely important and the second in terms of the tool selection. Of course I mean you need to set your objectives, clear KPIs, and keep on fine tuning the plan continuously for the next say it's a there's a window of 45 days you need to be really agile in terms of understanding the specifics of the digital channel which one is giving you the right objective delivery and which one is more expensive which is giving you, you know, more efficiency, you need to know all these things very clearly and the data is there for you to see specifically in digital communication and and do your tweaks so that you optimize your ROI. So that's that that's the approach that we need to take. Mr. Arora quickly to you on this part of, you know, standing out and getting noticed amidst the noise that festive promotions have. What are your two bits about it? I think going forward this festive season I think it will be more about telling than selling. So storytelling to the right audience is wonderful. Yeah, so storytelling to the right audience at the right time at the right place is I think is the key. I believe content will play a very, very important role in this entire decision life cycle. Yeah, everyone is so tired of, you know, watching screens these days. So the right content recommendation is I think will be the I think the new King of the Cune of this festive season, where you need to hit hard and hit that right time to write your comments because, as I said, everybody's so tired, because everything your entire decision cyclist is you're searching on mobile, you're searching on desktop and then you're buying it online itself. So journey has to be so you touch with them, get the right ball at right context, and then close it. Right. Perfect. My final question to all of you is that we have a lot of market here digital market as we are who are part of this discussion who are listening to us right now. To everyone one closing thought that you would like to share with them starting with you. One closing thought. Okay, so it would be very simple.  That's it. Wonderful. I think before a digital marketer you are a marketer. And for that your consumer decision journey should match to your consumer digital journey. If these two are actually talking to each other, your job is done. I think it's a personal experience and I think I would urge all the digital marketers today to sort of adhere to it is don't run after this entire sham off digital is a very fast word and you should keep changing creatives and keep amending your plans every now and then it doesn't work out like that. Give it at some time. It will happen. You will get to know in a few days when it's working on also don't any don't let anybody convince you about the fact that you know what you keep changing creatives every day and it's going to work wonders for you. It does not work wonders for anybody for that matter. My two bits will be matching content to intent so basically segment the consumer journey devise your creatives as per the, the stages of awareness interest desire and action and follow a systematic path, understanding the consumers sentiments at each stage and providing him the right inputs, so that he can take the right decision and I think that's that's the key. Lovely content and intent and telling what the telling I mean wonderful.  I think full funnel approach as with Mr. Dharma was talking about so looking at from a visibility perspective. To the entire purchase perspective. It is very important for for every marketer and everybody from publisher side is to look at that perspective very closely and master out so that we everybody is learning right now to be able to learn, relearn, evolve, and then keep doing it so I think the second option is I will say it's going to be innovation, experimental innovation for during test season where people are changing people are trying to so for example there's a concept called events tourism, where people are suddenly going out so we see behavior as they're going in different directions together. So it is very very important for my perspective to keep you know waiting keep experimenting with the stuff, especially digital because very dynamic what what I will say. So that I think holds to and this should be the key for this festive season. Thank you so much. Thank you, Mr. I'm sure that a lot of the audience has taken away a lot of critical insight as we enter the festive mood and we will continue to bring in more such virtual for now round table where we have exposed to that. Thank you everyone for joining us today. Thank you so much everybody.


For giving me this opportunity to present my work here So I'll be talking on bounds for the reduction number of primary ideals in dimension three and In dimension three because These statements are there for high dimensions as well, but it is more interesting in dimension three for dimension less than equal to two Results are already known. So I need my basic setup for that So throughout the talk R is a Noetherian local ring of positive dimension and I is an M primary ideal now a sequence of ideals is Called an eye admissible filtration if It satisfies these three properties so the first one just says that it is Decreasing filtration and the second one is the multiplicative property and the third one is what makes it eye admissible So for a filtration we define reduction Reduction is an ideal J such that J i n is equal to i n plus one for all n large and And it is called minimal reduction if it is minimal with respect to containment among all the reductions So when the residue field is infinite then minimal reductions exist and therefore We assume for all our statements that Residue field is infinite. There is a standard way to reduce the problem to that case Okay now to keep track of these indices to Keep track of these in the incidence and here we define the reduction number so basically This equality ensures that the result of I will be finitely generated over the result of J And the generators will have degree at most N at most The the value of n where after which it becomes equal so that number is preserved in the invariant reduction number So we define the reduction number of I with respect to J as Supremum of All the values n such that I n is not equal to J i n minus 1 Okay, so it is an important problem to give bounds on this reduction number and Desireively computable bounds So one such bound is known in terms of Hilbert coefficients So let me define Hilbert coefficients for any i admissible filtration. We look at this length function Length of our mod I n and this is known as the Hilbert Samuel function of I Then it is well known that there is a polynomial this this function this length function is of polynomial type Which means that there is a there is a polynomial with rational coefficients Such that this length function coincides with this polynomial For all the large values of n and this polynomial will have degree D, which is the dimension of the ring And this is a rational polynomial and in fact We can normalize the coefficients and then we can write it in this fashion Where all the coefficients are? Integers so this e i i's are integers and these coefficients are known as the Hilbert coefficients of I so it looks like that these Hilbert coefficients are Invariance of asymptotic powers of I I mean the asymptotic ions for this filtration But it turns out that these are very important and they contain a lot of information very deep in information about the structural properties of the filtration I or the ring and even the blow-up algebras of I So We restrict ourselves for the stock to the i-addict filtration so we always consider I is the powers of I The I is the filtration defined by the powers of I then Yeah, so now going back to the reduction number So if R is one-dimensional coin Macaulay local ring then R I is less than equal to E naught I minus one This R I is a minimum of all the reduction numbers Rji's which I defined earlier so R I is less than equal to E naught minus one Later Vaskuncelos proved that in any dimension positive dimension This R I is bounded above by D times multiplicity of I by order of I minus 2d plus 1 Where order is defined as the largest positive integer n such that I is contained in m to the power n Okay, and this is the best bound known for reduction number In higher dimension, but we will see that this is a large bound. This is large This is larger than what we have got Okay, and a non-cohen Macaulay version of the above results can also be found in literature so Now Rossi proved that the reduction number is less with respect to a Minimal reduction J is less than equal to the first Hilbert coefficient even minus the multiplicity E naught plus length of R mod I plus one and This is true only when dimension is at most two Okay, and here is this year is not correct. This is not 1988. This is 1999 or 2000 maybe so This this bound was given in terms of the first Hilbert coefficient and the multiplicity. This is a linear bound. It is nice and it is computable But it is known only for dimension at most two For D greater than equal to three. It is believed to be true. No counter examples are known But it is an open problem Okay, so our motivation was to understand the difficulties in extending the proof of Rossi for this bound in dimension larger than two and And we figured out that there are two major difficulties The first one is when the first one is that the reduction number does not behave well with respect to superficial elements Which means that this say I say are I write R prime as R mod X where X is a superficial element Then R of IR prime and R of I These are related in this manner and this inequality is not useful for this for us We would like to know a precise relation between these two if we want to follow the proof of Rossi but in general there are no Relation clear relation between these two invariants and the next problem is that the Ratliff rush filtration of I Which I will not define It does not behave well with respect to superficial elements, which means that these two operations do not commute I and tilde R prime is not equal to I and R prime tilde for all and greater than equal to one so if we Get hold of these two difficulties then we can prove Rossi's bound and there are some cases when we can get rid of these two difficulties For example, these are the cases So when depth of so in dimension three now if depth of gi is greater than equal to one or if depth of the associated grid a ring of the Ratliff rush filtration is Greater than equal to two or if the second and the third Hilbert coefficient vanish Or if e2i vanish and I is asymptotically normal or e2i is zero and gi is generalized coin Macaulay so in all these cases we get that Rossi's bound hold in dimension three and Basically, what is happening is those two problems, which I Stated can be handled in these cases So but of course these are very restrictive conditions and we would like to Get we would like to get rid of these conditions or We would like to get Some bound on reduction number without putting a strong hypothesis So so and there is a hope because we noticed that Yeah, if depth of gi is positive then the reduction numbers are preserved going modular superficial element but this relation holds even if depth of gi is zero and Here is an example for that This is taken from a work of Rossi and Walla. So in this case depth of gi is zero But this is dimension two case depth of gi is zero, but reduction number Modular superficial element is the same So basically we have to look at the question that when does it happen that? Reduction numbers are preserved Okay All right, so we tried to find relation between the reduction numbers and we got this useful lemma So in a Noetherian local ring of dimension D Positive dimension D and also positive depth We have that if if reduction number of I mod X is strictly less than reduction number of I Then in this interval Which is closed from left side and open from the right side I until I is not equal to I in Okay, and using this lemma now if I define this Invariant rho i which is minimum of i greater than equal to 1 such that iron is equal to i and tilde for all n greater than equal to i Then we get that if rho i is less than equal to rji minus 1 then Rossi's bound holds Okay, and again, this is a restriction here For rho i and this is not in general true. So we have examples when this is not true So And also examples where this is true. So again, there is some restriction on the ideal So this is one more case in that list which I displayed earlier When Rossi's bound hold in dimension 3 Okay, so then moving on in our effort to find the relation between the reduction numbers We could show that if depth of g i t is positive for some t greater than equal to 1 then Reduction numbers are related in this manner Okay, and in particular we can always put this t to be equal to rho i and therefore Rji is always less than equal to r i mod X plus rho i minus 1 So then using this we could generalize the the first condition on the list I displayed To the following theorem that if depth of g i t is positive for some t greater than equal to 1 which always happens Then rji is less than equal to even minus e naught plus length of r mod i plus t in dimension 3 So this is a linear bound Which we have got moreover we can further reduce it looking at the value of the reduction number I mean suppose if we know that reduction number is k mod t for some k between 1 and t minus 1 then this t can be replaced by k here and particularly useful corollary is that if depth of gi square is positive and The reduction number is odd then again we get Rossi's bound here. All right So here is an example which shows that the bound So in this case this depth of gm cube is greater than equal to 1 and therefore by our result This is the upper bound with plus 3 here For reduction number which turns out to be 7. However, if we calculate Vaskan's loss is bound. This is 19 So this new bound is better in this case All right Okay, so but ideally we want to remove all the hypothesis and get a bound So here is the result for a Cohen Macaulay local ring of dimension larger than 2 strictly larger than 2 Suppose depth of gi is greater than equal to d minus 3 then rji is less than equal to this Rossi's bound plus some new terms Which is e2 minus 1 times e2i minus e3 of i Okay, so so the second and the third Hilbert coefficient Here come into picture when we move to dimension 3 Okay, and in particular for small values of e2 here we get linear bound say when e2 is 0 or e2 is 1 Then this is a linear bound This so ideally we want a linear bound but here in our result we have got a quadratic term here of e2 squared Okay, so in dimension 3 this is an interesting result without any hypothesis on i Okay, and then Yeah, so as I said when e2 is 0 or 1 and 2 so for these small values we are getting linear bounds here Okay, now one would also Observe that this this additional term present here e2 minus 1 times e2 minus e3 of i This must be a non-negative term. Otherwise otherwise Rossi's bound is proved in dimension 3, which is Not believable. So we suspect that this is greater than equal to 0 for any m primary ideal But we could prove it only for integrally closed ideals So this gives a bound on e3 of i an upper bound on e3 of i It is e3 of i is less than is less than equal to e2 into e2 minus 1 for integrally closed ideals Okay, so okay, so the the difficulty as I mentioned is that the Ratley-Fresch does not behave well with respect to superficial elements and Yeah, so and then some if we get rid of that then again we get Rossi's bound So one such condition is when e2 and e3 vanishes and this was proved by Tony that in dimension 3 If e2 and e3 Becomes zero then Ratley-Fresch filtration behaves well modular superficial element But if i is integrally closed then e2 is zero Implies that gi is Cohen Macaulay. So this is a strong condition and it does not differentiate between Cohen Macaulay Associated graded rings and I mean non Cohen Macaulay cases. So This is not desirable. This is too strong Okay, so in fact for integrally closed ideals We we get some necessary and sufficient conditions for the Ratley-Fresch filtration of I Behaving well modular superficial element and one such result is the following Let R be a Cohen Macaulay local ring of dimension greater than equal to 3 and I is an M primary ideal then The Ratley-Fresch filtration behaves well If the Ratley-Fresch filtration behaves well modular superficial sequence, then we have this inequality This inequality was earlier known when with the condition that depth of gi is greater than equal to D minus 1 So this provides a necessary condition for checking where the Ratley-Fresch behaves well Okay, and Here is an example where we can apply this. So in this example This e3 is minus 1 and e2 minus even plus e not minus length of our mod maximal ideal is 0 So the inequality is not satisfied and therefore the Ratley-Fresch of the maximal ideal does not behave well Modular superficial element Okay, but for our problem we need sufficient conditions So we prove this these interesting bounds on e3 of I For integrally closed ideals so if I is an integrally closed M primary ideal and J is a minimal reduction of I then we have these three bounds on e3 of I and Here if you notice that Four so they are not related to each other directly I mean there are some indirect relations because from four we can get to five if we know that Rossi's bound holds in dimension three But we do not know that even then we can prove this bound okay which is a computable upper bound for e3 and Then for integrally closed ideals we know that e2 is larger than even minus is greater than equal to even minus e not plus length of our mod I and so we can bound this number by e2 of I but in fact We can actually bound e3 of I by e2 minus 1 by 2 times this Okay, and so these are interesting bounds and what is more interesting is that if In dimension three if equality holds in any one of four five or six then the Ratley-Fresh filtration of I behaves well modulo a superficial element and Consequently Rossi's bound will hold Okay, so these are some computable at least five and six are computable conditions When we can be sure that Rossi's bound holds Okay, and we have the converse statements as well suppose the Ratley-Fresh filtration behaves well modulo a superficial sequence x1 x2 xd minus 2 Then equality holds in four provided RGI is less than equal to three equality holds in five provided Even minus e not plus length of our mod is less than equal to two and equality holds in six provided e2 of I is less than equal to three okay, so This is for integrally closed M primary ideals and in fact we could actually Improve the bound for integrally closed ideals So in that case the hypothesis is same I is integrally but I is integrally closed and Depth of GI is greater than equal to D minus 3 then now RGI is less than equal to the Rossi's bound plus this term and This term is a smaller than e2 into e2 minus 1 minus e3 of I the earlier bound Okay, so this is the best we can have and Rossi's bound still remains open and mystery for us so That's all and then we have some Generalizations in Noetherian for Noetherian local rings So this bound of Rossi in even in dimension has been equal to two is not known for filtration and for Noetherian local rings If we assume that the ring is book bomb then we can have some bounds so in one So, okay, so this is last slide. I'll just continue if R is one-dimensional book bomb local ring Then we have Rossi's bound With some additional terms here. So even I minus even J Minus enotype plus length of arm or die plus two so in place of plus one we have plus two and even J will appear here this is a standard thing it appears everywhere and Then for two-dimensional book bomb local ring Again if we assume that depth of GIT is positive for some T greater than equal to 1 then RGI is less than equal to even minus even J minus enotype plus length of arm or I plus T plus 1 so this T will appear here Okay, and That's all so these are some references and All these results were joint work with the Mosme Wandel and Anud Kumar Yadav Thank you very much