School of Technology and Computer Science - PhD Thesis Seminar
https://brahma.tcs.tifr.res.in/event/phd-thesis-seminar
enHardness and Independence of Polynomials
https://brahma.tcs.tifr.res.in/events/hardness-and-independence-polynomials-0
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/prerona-chatterjee">Prerona Chatterjee</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thursday, 17 March 2022, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2022-03-17T14:30:00+05:30">14:30</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2022-03-17T15:30:00+05:30">15:30</span></span></span></div></div></section><section class="field field-name-field-venue field-type-taxonomy-term-reference field-label-inline clearfix view-mode-rss clearfix">
<h2 class="field-label">Venue: </h2>
<ul class="field-items">
<li class="field-item even">
<a href="/venue/person-rno-ag-66-and-also-zoom" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">in person @ R.No. AG-66 and also via Zoom</a> </li>
</ul>
</section>
<section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/ramprasad-saptharishi">Ramprasad Saptharishi</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Algebraic Complexity Theory is a field in which one studies complexity theoretic questions surrounding algebraic objects. In this talk we will be broadly discussing two such problems.</p>
<p>The first problem is showing lower bounds for explicit polynomials against various algebraic computational models. The most natural and well studied models of computation are algebraic circuits, algebraic branching programs (ABPs) and algebraic formulas. With respect to proving lower bounds against these models, we show the following results.<br />
1. Any algebraic branching program computing \sum_{i=1}^n x_i^n must have at least n^2 vertices. The previous best known lower bound was \Omega(n log n) on the number of edges for the same polynomial [Baur-Strassen].<br />
2. Any formula computing the elementary symmetric polynomial of degree 0.1n must have at least n^2 vertices. The previous best lower bound for any multilinear polynomial was \Omega(n^2/log n) [Nechiporuk, Kalorkoti]. It can also be shown that previous known methods can not prove a bound better than \Omega(n^2/log n) for any explicit multilinear polynomial.<br />
This is joint work with Mrinal Kumar, Adrian She and Ben Lee Volk.</p>
<p>Along with proving lower bounds against these models, studying their relative powers is also an important problem in algebraic circuit complexity. It is known that formulas can be efficiently simulated by ABPs and checking whether the converse of this statement holds is a central question in the field. We make progress towards solving this problem in the non-commutative setting, where we show a tight super-polynomial separation between ABPs and some structured formulas.</p>
<p>The second problem that we are interested in relates the questions of checking whether a given algebraic compuational model is computing the zero polynomial or not and checking whether a given set of polynomials is algebraically independent or not. The connection between these questions is via the notion of Faithful Homomorphisms. Although construction of faithful homomorphisms were known when the underlying field had characteristic zero [Beecken-Mittman-Saxena, Agrawal-Saha-Saptharishi-Saxena], they were not known in the setting where the underlying field had finite characteristic since efficient algorithms to check algebraic indepndence were not known in this setting. Following up on the work of Pandey, Saxena and Sinhababu, we construct faithful homomorphisms over fields of finite characetristics in some restricted settings and as a consequence show efficient polynomial identity tests for related models of computation. This is joint work with Ramprasad Saptharishi.</p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Mon, 14 Mar 2022 05:12:19 +0000Supriya Pottipati4627 at https://brahma.tcs.tifr.res.inFourier Analytic Techniques in Machine Learning
https://brahma.tcs.tifr.res.in/events/fourier-analytic-techniques-machine-learning
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/somnath-chakraborty">Somnath Chakraborty</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Wednesday, 12 January 2022, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2022-01-12T09:00:00+05:30">09:00</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2022-01-12T10:00:00+05:30">10:00</span></span></span></div></div></section><section class="field field-name-field-venue field-type-taxonomy-term-reference field-label-inline clearfix view-mode-rss clearfix">
<h2 class="field-label">Venue: </h2>
<ul class="field-items">
<li class="field-item even">
<a href="/venue/zoom" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Via Zoom</a> </li>
</ul>
</section>
<section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/hariharan-narayanan">Hariharan Narayanan</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>In this talk, we will discuss the following two problems.</p>
<p>Problem 1. Given independent random samples drawn from an (almost uniform) mixture of at most k spherical d-dimensional Gaussians of unit variance, can we devise an efficient algorithm that recovers the center's within arbitrary accuracy?</p>
<p>Problem 2. How can we integrate in the class of Lipschitz functions on d-dimensional sphere, computationally efficiently?</p>
<p>Efficient algorithms are known to deal with the first problem in the constant dimensions. We show that in the regime d= log k, Fourier analytic ideas can be employed to obtain an efficient algorithm, provided that minimum separation of the center's of the individual Gaussian components is O(✓d). This minimum separation is known to be optimal.</p>
<p>For the second problem, we find a computationally efficient method of finding an equidistributed net on a d-dimensional sphere. The techniques are inspired by work of Landau-Russell (2004) which used ideas from Fourier analysis on finite groups to get a quantitative improvement on the Alon-Roichman theorem that says a random Cayley graph is an expander.</p>
<p>These results are based on joint work with Hariharan Narayanan.</p>
<p>Join Zoom Meeting<br /><a href="https://zoom.us/j/97251350514?pwd=UVA5aTR4eFlZTVpER2dFRnZoRXJDUT09">https://zoom.us/j/97251350514?pwd=UVA5aTR4eFlZTVpER2dFRnZoRXJDUT09</a></p>
<p>Meeting ID: 972 5135 0514<br />
Passcode: 844383</p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Mon, 10 Jan 2022 11:58:44 +0000Supriya Pottipati4597 at https://brahma.tcs.tifr.res.inExact Sampling and List-Decoding
https://brahma.tcs.tifr.res.in/events/exact-sampling-and-list-decoding
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/siddharth-bhandari">Siddharth Bhandari</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Friday, 10 December 2021, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2021-12-10T09:00:00+05:30">09:00</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2021-12-10T10:00:00+05:30">10:00</span></span></span></div></div></section><section class="field field-name-field-venue field-type-taxonomy-term-reference field-label-inline clearfix view-mode-rss clearfix">
<h2 class="field-label">Venue: </h2>
<ul class="field-items">
<li class="field-item even">
<a href="/venue/zoom" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Via Zoom</a> </li>
</ul>
</section>
<section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/prahladh-harsha">Prahladh Harsha</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>In this thesis defense, we will discuss the following results.</p>
<p>1. Exact sampling: We will present an efficient algorithm that, given a graph of maximum degree $\Delta$ and a list of at least $3\Delta+1$ colours, produces a random colouring of the graph that is \emph{exactly} uniformly distributed on the set of all proper colourings. Before this work, it was known that exact sampling was possible if about $\Delta^2$ colours were allowed.</p>
<p>2. List-decoding error-correcting codes: In list-decoding, the decoder, based on the received word, is required to output a small list of messages, one of which must be the original message. We will discuss the following results about list-decoding.</p>
<p>(a) Zero-error list decoding capacity of the $q/(q-1)$ channel: We will present a lower bound showing that the zero-error list decoding capacity of this channel is exponentially small in $q$ even if the list size is allowed grow as $\frac{1}{6} q \ln q$. Previous results showed that the capacity was exponentially small if the list size was allowed to grow no larger than $1.58q$.</p>
<p>(b) Multiplicity codes: We consider a natural generalization of Reed-Muller codes where at each evaluation point, one records not only the evaluation of the message polynomial, but also all its partial derivatives up to a certain order. We will present an efficient algorithm that (under mild assumptions) list-decodes multivariate multiplicity codes on arbitrary grids up to their distance. Previously such results were known only for univariate multiplicity codes.</p>
<p>(c) Polynomial ideal codes: A polynomial ideal code is specified by a collection of relatively prime monic polynomials. The encoding is obtained by specifying the remainders of the message polynomial modulo the various polynomials in the collection. We will describe an efficient algorithm to list-decode some special polynomial ideal codes, which we \emph{call affine folded Reed-Solomon codes,} up to their distance. Previous results allowed list-decoding up to the distance for folded Reed-Solomon codes, univariate multiplicity codes and additive folded Reed-Solomon codes, which are all instances of affine folded Reed-Solomon codes.</p>
<p>(The above results were obtained in collaborations that involved the<br />
following: Sayantan Chakraborty, Prahladh Harsha, Mrinal Kumar, Jaikumar Radhakrishnan, Madhu Sudan.)</p>
<p> Zoom link: <a href="https://zoom.us/j/95587295066?pwd=ZW5QQ1NrSVEwOG5iZzloVTlMV2ZBZz09">https://zoom.us/j/95587295066?pwd=ZW5QQ1NrSVEwOG5iZzloVTlMV2ZBZz09</a></p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Tue, 07 Dec 2021 05:53:36 +0000Supriya Pottipati4592 at https://brahma.tcs.tifr.res.inPartial Function Extension with Applications to Property Testing and Learning
https://brahma.tcs.tifr.res.in/events/partial-function-extension-applications-property-testing-and-learning
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/gunjan-kumar">Gunjan Kumar</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thursday, 2 December 2021, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2021-12-02T18:00:00+05:30">18:00</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2021-12-02T19:00:00+05:30">19:00</span></span></span></div></div></section><section class="field field-name-field-venue field-type-taxonomy-term-reference field-label-inline clearfix view-mode-rss clearfix">
<h2 class="field-label">Venue: </h2>
<ul class="field-items">
<li class="field-item even">
<a href="/venue/zoom" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Via Zoom</a> </li>
</ul>
</section>
<section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/umang-bhaskar">Umang Bhaskar</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Partial function extension is a basic problem that underpins multiple research topics in optimization, including learning, property testing, and game theory. Here, we are given a partial function consisting of some points from a domain and a function value at each point. Our objective is to determine if this partial function can be extended to a function defined on the domain, that additionally satisfies a given property, such as monotonicity. We formally study partial function extension for various complement-free functions.</p>
<p>Our contributions are twofold. Firstly, for the properties studied, we give a combinatorial characterization and bounds on the complexity of partial function extension. Secondly, we develop new connections between partial function extension and learning and property testing, and use these to give new results for these problems.</p>
<p>Join Zoom Meeting</p>
<p><a href="https://zoom.us/j/96720853429?pwd=ZUFFdzYvSmQzMWRNOG9PZVNzMHJpdz09">https://zoom.us/j/96720853429?pwd=ZUFFdzYvSmQzMWRNOG9PZVNzMHJpdz09</a></p>
<p>Meeting ID: 967 2085 3429<br />
Passcode: 869836</p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Tue, 30 Nov 2021 05:01:21 +0000Supriya Pottipati4588 at https://brahma.tcs.tifr.res.inAn Asymptotic Analysis of Risk in Financial Systems - Analysis and Algorithms
https://brahma.tcs.tifr.res.in/events/asymptotic-analysis-risk-financial-systems-analysis-and-algorithms
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/anand-deo">Anand Deo</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Wednesday, 25 August 2021, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2021-08-25T18:30:00+05:30">18:30</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2021-08-25T19:30:00+05:30">19:30</span></span></span></div></div></section><section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/sandeep-k-juneja">Sandeep K Juneja</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Over the past few decades, probabilistic models have become an important tool for under-standing risks and decision making in practical ﬁnancial systems. In the design of such systems one often wishes to relate the risk to the statistics of underlying stochasticity. However, this task is complicated by the fact that realistic ﬁnancial systems are complex, and undesirable events in them are often rare. A large body of research has been devoted to understanding the nature of such rare events, and how they relate to the stochasticity aﬀecting the system. In this talk, we undertake a detailed study of these aspects in order to develop structural insights on a number of ﬁnancial systems of practical interest. Our main contributions are as below:<br />
I. We discuss the development of a closed form, interpretable parameter estimation technique for predicting defaults of ﬁnancial ﬁrms. Typically, one uses maximum likelihood estimation (MLE) for predicting the ﬁrm default probabilities. We prove that our estimator is almost as accurate as the MLE, verify our result empirically on a sample of US corporate data, and showcase the computational/interpretative beneﬁts of our estimator over the MLE.<br />
II. We develop a statistically consistent estimator for conditional value-at-risk (CVaR) based optimization objectives and their gradients. Unlike the state-of-the-art sample average approximations, the proposed approximation scheme exploits the self-similarity of heavy-tailed distributions to extrapolate data from lower quantiles, thereby reducing data requirements for accurate estimation.<br />
III. Motivated by the increasing adoption of models which facilitate automation in risk management and decision-making, we present a novel importance sampling (IS) scheme for measuring distribution tails of objectives. Conventional eﬃcient IS approaches suﬀer from feasibility concerns due to the need to intricately tailor the sampler to the underlying probability distribution and the objective. We overcome this challenge in the proposed black-box scheme by automating the selection of an eﬀective IS distribution with a transformation that implicitly learns and replicates the concentration properties observed in less rare samples.<br />
IV. We develop a limiting representation for an interconnected banking network in presence of partial information. Practical banking networks are large and complicated, and one searches for simple limiting representations (as the network size goes to inﬁnity). We characterise the wealth of banks in a large network in terms of a simple, one dimensional distributional ﬁxed point, which we show is amenable to Monte Carlo simulation.<br />
This talk is based on joint work with Sandeep Juneja and Karthyek Murthy.</p>
<p> The zoom link for the talk is <a href="https://zoom.us/j/93128173558?pwd=SXRkdFE1MVBnc2hSSEtvbHRIZG4yQT09">https://zoom.us/j/93128173558?pwd=SXRkdFE1MVBnc2hSSEtvbHRIZG4yQT09</a></p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Wed, 18 Aug 2021 05:13:28 +0000Supriya Pottipati4542 at https://brahma.tcs.tifr.res.inHitting Sets for Algebraic Models: Constructions and Consequences
https://brahma.tcs.tifr.res.in/events/hitting-sets-algebraic-models-constructions-and-consequences
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/anamay-tengse">Anamay Tengse</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Wednesday, 9 June 2021, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2021-06-09T14:30:00+05:30">14:30</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2021-06-09T15:30:00+05:30">15:30</span></span></span></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>We study hitting sets for polynomials computed by several algebraic models. For a class of polynomials C, hitting sets for C capture the problem of deterministic blackbox PIT for C: checking if a polynomial f from C is zero by querying f on a few points. Formally, H is a hitting set for a class C, if for every nonzero f in C, there is some point h in H for which f(h) is nonzero. Owing to its close connections to the search of explicit hard polynomials, finding small, explicit hitting sets for various classes of polynomials is a central question in algebraic complexity theory.</p>
<p>Our contributions towards the study of hitting sets are as follows. We provide two explicit constructions of hitting sets: quasipolynomial sized hitting sets for 'UPT circuits', and poly-sized hitting sets for log-variate 'depth-3-powering circuits'. Next, we show that for any general enough algebraic model, like circuits or formulas, even a mild improvement to the trivial hitting sets for the model leads to almost efficient, explicit hitting sets for that model. Lastly, we explore how non-trivial hitting sets for a class of polynomials help us in proving lower bounds against that class.</p>
<p>The talk will be based on my joint works with Prerona Chatterjee (TIFR), Mrinal Kumar (IITB), C. Ramya (TIFR) and Ramprasad Saptharishi (TIFR).</p>
<p>Zoom link: <a href="https://zoom.us/j/92326426336?pwd=V2h0WGpUeklMd01Mak1sVGpvTm9QUT09">https://zoom.us/j/92326426336?pwd=V2h0WGpUeklMd01Mak1sVGpvTm9QUT09</a></p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Sat, 05 Jun 2021 10:42:02 +0000Supriya Pottipati4508 at https://brahma.tcs.tifr.res.inCommunication Complexity and Quantum Optimization Lower Bounds via Query Complexity
https://brahma.tcs.tifr.res.in/events/communication-complexity-and-quantum-optimization-lower-bounds-query-complexity
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/suhail-sherif">Suhail Sherif</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Monday, 17 May 2021, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2021-05-17T17:00:00+05:30">17:00</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2021-05-17T18:00:00+05:30">18:00</span></span></span></div></div></section><section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/arkadev-chattopadhyay">Arkadev Chattopadhyay</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>The query model is a simple model of computation that has led to many deep results. One such class of results relates computational complexity measures such as query complexity/communication complexity to algebraic measures such as degree/rank. The first part of this thesis deals with such relations. The results of this part of the thesis are given below.</p>
<p>1. In the context of randomized communication complexity and randomized parity decision tree (RPDT) complexity, we prove that the relevant computational measures and algebraic measures are not closely related. This disproves multiple long-standing conjectures in communication complexity.</p>
<p>2. We try to quantitatively strengthen the above result. We do manage to do so in the context of RPDTs, but there are challenges in translating this strengthening to the context of randomized communication complexity. We pose a fundamental conjecture that would imply that the strengthening holds in the communication world as well.</p>
<p>In the second part of the thesis, we look at convex optimization. The goal is to optimize a convex function in a bounded region when you can only learn about the function through function value and gradient queries. We want to use as few queries as possible. Projected gradient descent (PGD) is a well-known algorithm that optimally solves this task when the dimension of the function's domain is large. In the second part of the thesis we add to the optimality results of PGD.</p>
<p>3. (a) In the case of quantum algorithms it was open whether there is a quadratic speedup over PGD when the dimension is large. We show that this is not so, that PGD is optimal up to constant factors.<br />
(b) In the case of randomized algorithms we show a simple argument bettering the range of dimensions where PGD is known to be optimal up to constant factors.</p>
<p>We end with a few open problems.</p>
<p>Join Zoom Meeting<br /><a href="https://zoom.us/j/93580606744?pwd=L1pCek1pSy91a0JOOXpXdjI0Z2EyQT09">https://zoom.us/j/93580606744?pwd=L1pCek1pSy91a0JOOXpXdjI0Z2EyQT09</a><br />
Meeting ID: 935 8060 6744<br />
Passcode: 335095</p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Wed, 05 May 2021 07:02:36 +0000Supriya Pottipati4500 at https://brahma.tcs.tifr.res.inFormalizing Finite Set Combinatorics in Type Theory
https://brahma.tcs.tifr.res.in/events/formalizing-finite-set-combinatorics-type-theory-0
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/abhishek-singh">Abhishek Singh</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Monday, 14 December 2020, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2020-12-14T10:30:00+05:30">10:30</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2020-12-14T11:30:00+05:30">11:30</span></span></span></div></div></section><section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/n-raja">N Raja</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Mathematical proofs when written in conventional ways often contain imprecise definitions, unstated background assumptions, and inferential gaps in reasoning. In such circumstances, it becomes difficult for a reviewer to determine whether the given proof is correct or not. Even if the theorem statement turns out to be true, judging it to be so could take a long time. A possible solution to this problem is to formalize mathematical results using Proof Assistants. Proof Assistants are software tools built on top of a small and trusted kernel that provides a formal language for writing mathematical statements and their proofs. Hence, formally verifying a mathematical theory using a Proof Assistant can increase our confidence in the verified results. However, the task of formalizing mathematics using Proof Assistants presents some unique challenges; both practical as well as theoretical. Theoretical challenges mostly arise because some trivially assumed axioms of classical mathematics may not be provable in the core logic of the Proof Assistant. On the other hand, the practical difficulties of formalization mostly arise because the machine-checkable proofs are significantly more detailed than the corresponding paper proofs. In this talk, we will address both these issues while presenting formal proofs of some key results from finite set combinatorics. More precisely, we present formalized libraries of definitions and results on two important mathematical structures from combinatorics: (i) finite partially ordered sets, and (ii) finite simple graphs. These libraries have been formalized in the type theory of Coq Proof Assistant.</p>
<p> Zoom Link:</p>
<p><a href="https://zoom.us/j/95365190349?pwd=ZENsRG1pbmVpV01nQ3BPRGJVZmZPdz09">https://zoom.us/j/95365190349?pwd=ZENsRG1pbmVpV01nQ3BPRGJVZmZPdz09</a></p>
<p>Meeting ID: 953 6519 0349<br />
Passcode: 993493</p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Fri, 11 Dec 2020 07:28:47 +0000Supriya Pottipati4438 at https://brahma.tcs.tifr.res.inSome Derandomized Constructions in Quantum Information Processing
https://brahma.tcs.tifr.res.in/events/some-derandomized-constructions-quantum-information-processing
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/aditya-nema">Aditya Nema</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Friday, 16 October 2020, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2020-10-16T13:30:00+05:30">13:30</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2020-10-16T14:30:00+05:30">14:30</span></span></span></div></div></section><section class="field field-name-field-organisers field-type-entityreference field-label-inline clearfix view-mode-rss"><h2 class="field-label">Organisers: </h2><div class="field-items"><div class="field-item even"><a href="/people/pranab-sen">Pranab Sen</a></div></div></section><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Randomness is a vital tool and resource in both classical and quantum information processing. However, constructing random bits is expensive, and hence minimising their use is desirable. Several tools have been developed in classical computing for this purpose. Two such tools are expanders and k-wise independent random variables, and they have already found many applications in classical computing. In this thesis we investigate the quantum analogues of these two tools for quantum information processing tasks.</p>
<p>In quantum information processing, algorithms are often modeled by unitary operators and randomness enters the picture from the choice of random unitary operators, much like randomness in classical information processing. Existential proofs in information processing applications are almost always based on unitary matrices drawn from the Haar probability measure on the unitary group (formalisation of the uniform measure on the unitary group). However, an n-qubit unitary is described by 4^n real parameters, and thus cannot be efficiently approximated using a sub-exponential amount of time or randomness. This has led to the construction of efficient pseudo-random ensembles<br />
of unitaries which emulate the Haar measure, up to the first t-moments, for certain applications [Harrow, Low 2009]. Such constructions are referred to as unitary t-designs. It is known that there are exact unitary 't'-designs for any t [Kuperberg, 2006]. The advantage of using these designs is that approximate unitary t-designs can be efficiently constructed for t = poly(log dimension) [Brandao et al. 2012, Sen 2018].</p>
<p>In this thesis we apply these designs for the following tasks:<br />
1. Showing that the minimum output Renyi p-entropy, for all p >= 1, of quantum channels is subadditive. Renyi 1-entropy is the well known von Neumann entropy and its subadditivity leads to quantum channels with superadditive classical Holevo capacity [Shor 2004]. We prove for the first time that approximate unitary n^{2/3}-designs lead to a quantum channel with superadditive classical Holevo capacity;</p>
<p>2. Efficient estimation of average gate fidelity of a quantum logic gate using few random bits, better than the state of the art;</p>
<p> 3. Concentration of measure for non-catalytic decoupling theorem in quantum information theory, using an approximate t-design for a suitable value of t, beating the state of the art for relative thermalisation under certain reasonable assumptions.</p>
<p>Although the unitary t-designs used in the above works have t larger than what is known to be efficiently implementable, yet in all cases they lead to significant savings in the number of random bits required vis-a-vis Haar random unitaries. Thus, all the three works can be thought of as steps towards their respective derandomisations.<br />
-------------------<br />
Zoom Meeting <a href="https://zoom.us/j/91958942801?pwd=QzdyN2RXbE1RQko1bVpMZGluYVdNUT09 ">https://zoom.us/j/91958942801?pwd=QzdyN2RXbE1RQko1bVpMZGluYVdNUT09 </a> Meeting ID: 919 5894 2801 Passcode: 631121</p>
</div></div></div><section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Thu, 08 Oct 2020 04:37:38 +0000Supriya Pottipati4422 at https://brahma.tcs.tifr.res.inCommunication Complexity of XOR Functions
https://brahma.tcs.tifr.res.in/events/communication-complexity-xor-functions
<div class="field field-name-field-event-type field-type-taxonomy-term-reference field-label-hidden view-mode-rss clearfix">
<ul class="field-items">
<li class="field-item even">
<a href="/event/phd-thesis-seminar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">PhD Thesis Seminar</a> </li>
</ul>
</div>
<section class="field field-name-field-other field-type-text-long field-label-inline clearfix view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Nikhil S. Mande</div></div></section><!--
THIS FILE IS NOT USED AND IS HERE AS A STARTING POINT FOR CUSTOMIZATION ONLY.
See http://api.drupal.org/api/function/theme_field/7 for details.
After copying this file to your theme's folder and customizing it, remove this
HTML comment.
-->
<div class="field field-name-field-members field-type-entityreference field-label-inline clearfix view-mode-rss clearfix">
<div class="field-label">Speaker: </div>
<div class="field-items">
<div class="field-item even"><a href="/people/nikhil-s-mande">Nikhil S Mande</a>, TIFR</div>
</div>
</div>
<section class="field field-name-field-time field-type-datetime field-label-inline clearfix view-mode-rss"><h2 class="field-label">Time: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Monday, 26 November 2018, <span class="date-display-range"><span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2018-11-26T09:30:00+05:30">09:30</span> to <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2018-11-26T10:30:00+05:30">10:30</span></span></span></div></div></section><section class="field field-name-field-venue field-type-taxonomy-term-reference field-label-inline clearfix view-mode-rss clearfix">
<h2 class="field-label">Venue: </h2>
<ul class="field-items">
<li class="field-item even">
<a href="/venue/ag-66" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">AG-66</a> </li>
</ul>
</section>
<section class="field field-name-field-diplay-profile field-type-list-boolean field-label-above view-mode-rss"><h2 class="field-label">Faculty Candidate: </h2><div class="field-items"><div class="field-item even"></div></div></section>Tue, 20 Nov 2018 09:10:10 +0000Supriya Pottipati4081 at https://brahma.tcs.tifr.res.in