Theoretical Statistics and Mathematics Unit

## Past month's Seminars and Colloquia

[Past seminars of this year] [Colloquia archive] [All Seminars archive]

### COLLOQUIUM

Title :Translation Invariant Diffusions
Speaker : B. Rajeev (ISI Bangalore)
Time : January 25, 2018 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : In this talk we will discuss the existence and uniqueness of a class of stochastic partial differential equations (SPDE) that generalize the classical Ito stochastic differential equations and also the SPDE in Rajeev (2013, IJPAM). We will discuss some applications and (time permitting) give an idea of the proofs of existence and uniqueness.

### COLLOQUIUM

Title :Extremals of inequalities and their uniqueness
Speaker : K. Sandeep (TIFR-CAM Bangalore)
Time : February 1, 2018 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : In this talk we will discuss some of the inequalities in Sobolev spaces and their extremals. We will focus on the question of classification of extremals for these inequalities.

### STUDENT SEMINAR

Title : Substance Use & Abuse: Consequences and Risks
Speaker : B N Sharada (Counsellor - Parivarthan)
Time : February 6, 2018 (Tuesday), 03:15 PM
Venue : Auditorium
Abstract : Any substance or product that affects the way people feel, think, see, taste, smell, hear or behave is called a Psychoactive Substance. The use of these substances can cause a change in the mental process of the individual and can subsequently affect the user’s health and life.

### COLLOQUIUM

Title :Disappearing coefficients and lacunae for hyperbolic polynomials
Speaker : Yuliy Baryshnikov (University of Illinois at Urbana-Champaign USA)
Time : February 8, 2018 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : Reading the coefficients of a generating function off from its singularities is a well-oiled machine in the case of one variable. In multivariate case, the theory is still being developed, and involves, besides complex analysis, insights from the theory of hyperbolic polynomials and their Fourier transforms. I will outline what is known, illustrating the story with the examples from "integrable combinatorics" (like Aztec diamond tilings), and report on a recent work (wit S. Melczer and R. Pemantle) on a puzzling appearance of lacunae in a symmetric generating function.

### COLLOQUIUM

Title :Pair correlation for Hecke eigenvalues
Speaker : Kaneenika Sinha (IISER Pune)
Time : February 12, 2018 (Monday), 02:00 PM
Venue : Auditorium
Abstract : Distribution of prime numbers is among the most important themes in mathematics. In the last few decades, this theme has evolved into fine questions about spacing between consecutive prime numbers. Such questions can be generalised to the values at prime numbers of important arithmetic functions. After a historical overview of such questions, we consider the spacing statistics for eigenvalues of Hecke operators $T_p$ ($p$ denotes a prime) acting on spaces of modular cusp forms with prescribed weights and levels. This is a report on joint work with Baskar Balasubramanyam.

### BANGALORE PROBABILITY SEMINAR

Title : Constrainted Determinantal Point Processes
Speaker : Amit Deshpande (Microsoft Research)
Time : February 12, 2018 (Monday), 02:15 PM
Venue : SSIU Seminar Hall
Abstract : Determinantal Point Processes (DPPs) have their origins in quantum physics and random matrix theory, and have also found practical applications in machine learning. DPPs define probability distributions over subsets of elements, exhibit negative correlation and other interesting properties, and have efficient sampling algorithms. In this talk, I will discuss some counting and sampling problems for DPPs with combinatorial constraints, and show their connections to other objects such as the mixed characteristic polynomials that arise in the proof of Kadison-Singer problem. Joint work with Elisa Celis, Tarun Kathuria, Damian Staszak, Nisheeth Vishnoi.

### BANGALORE PROBABILITY SEMINAR

Title : A probabilistic approach to Voronin's universality theorem.
Speaker : Bhaskar Bagchi (Indian Statistical Institute Bangalore)
Time : February 12, 2018 (Monday), 03:30 PM
Venue : Auditorium
Abstract : The universality theorem on the Riemann Zeta function states that any non-vanishing holomorphic function on the strip 1/2 < Re(z) < 1 can be arbitrarily well approximated (in the topology of locally uniform convergence) by vertical translates of Zeta. In this talk I intend to discuss the probabilistic approach to this theorem given in my Ph.D. thesis. This approach actually proves a very much stronger version of the universality theorem.

### COLLOQUIUM

Title :An invariance principle for sums and record times of regularly varying stationary sequences
Speaker : Philippe Soulier (University Paris Nanterre)
Time : February 15, 2018 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. This allows to prove a new functional limit theorem. Its assumptions are satisfied by a wide class of applied time series models, for which standard limiting theory in the space D of cadlag functions does not apply. We further apply our method to analyze record times in a sequence of dependent stationary observations, even when their marginal distribution is not necessarily regularly varying. Under certain restrictions on dependence among the observations, we show that the record times after scaling converge to a relatively simple compound scale invariant Poisson process. Joint work with Bojan Basrak and Hrvoje Planinic (both in Zagreb University).

### BANGALORE PROBABILITY SEMINAR

Title : Stochastic PDEs in S' for SDEs driven by Levy noise
Speaker : Suprio Bhar (TIFR-CAM)
Time : February 19, 2018 (Monday), 03:15 PM
Venue : Auditorium
Abstract : In this talk, we will discuss recent results on the existence and uniqueness of strong solutions of a class of stochastic PDEs driven by finite dimensional L\'evy noise. These stochastic PDEs arise from finite dimensional SDEs driven by the same L\'evy noise and the strong solutions have the `translation invariance' property. Our results extend similar correspondences proved in [Rajeev, \emph{Translation invariant diffusion in the space of tempered distributions}, Indian J. Pure Appl. Math. \textbf{44} (2013), no.~2, 231--258] for diffusion processes. We will focus on the uniqueness results, which follow from a criterion called the 'Monotonicity inequality'. This is joint work with B. Rajeev and Barun Sarkar.

### STUDENT SEMINAR

Title : Away from the Average: The Physics of Fluctuations
Speaker : Mustansir Barma (TIFR Centre for Interdisciplinary Sciences - Hyderabad)
Time : February 23, 2018 (Friday), 03:15 PM
Venue : Auditorium
Abstract : Fluctuations often tell more about a statistical system than do the average values of observables. In this lecture, I will highlight the role played by fluctuations in bringing about the remarkable universality observed near the critical points of many systems (fluids, magnets …). Further, one might expect ordering to be destroyed by fluctuations larger than the average. While this statement is almost always true, there are interesting exceptions; such exceptionally interesting systems will also be discussed.

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