Upcoming Seminars
Math Seminar: On the moving sofa problem
Jineon Baek, University of Michigan
Thursday, April 11, 2024
12:45 – 1:45 PM (Free Period)
Armitage Hall, Room 123
Abstract: Modeling the situation of moving furniture around, the moving sofa problem asks for the maximum area of a planar shape that can move around the corner in an L-shaped hallway of width 1. The problem was posed by Leo Moser in 1966, and the best known lower bound of 2.2195… was proved by Gerver in 1994, by constructing a sofa whose boundary consists of 18 special curves. While it is conjectured that Gerver’s sofa attains the maximum area, the best published upper bound of 2.37 was proved by Kallus and Romik in 2018 using computer assistance.
Improving upon the computer-assisted approach of Kallus and Romik, we improve the upper bound to 2.32. Moreover, without any computer assistance, we prove a conceptually new upper bound of $1 + \pi^2/8$ = 2.2337… that is much closer to the lower bound of Gerver, on a large subset of shapes which includes Gerver’s sofa. We also discuss the possibility of making the upper bound of 2.2337… unconditional by building upon the approaches of the two results.
Past Seminars
Math Seminar: The polynomial method in the study of zero-sum theorems
Dr. Sukumar Das Adhikari
Friday, November 17, 2023
1:30 PM – 2:30 PM
BSB 132
We consider some elementary algebraic techniques in the area of Zero-sum Combinatorics. Originating from a beautiful theorem of Erdos-Ginzberg-Ziv about sixty years ago and some other questions around the same time, it has found various ramifications and generalizations, with many interesting results and several unanswered questions. It has ushered in many algebraic as well as combinatorial techniques which have found other applications also. In this talk, we shall report on applications of some elementary algebraic techniques in addressing some questions related to a weighted generalization.
Math Seminar: Infinite-dimensional Wishart processes
Dr. Sonja Cox, Korteweg-de Vries Institute for Mathematics, University of Amsterdam
Friday, October 20, 2023
11:20 AM – 12:20 PM
BSB 132
A Wishart process is a stochastic process $(X_t)_{t\geq 0}$ taking values in the space of positive semi-definite matrices such that $X_t$ has a (generalized) Wishart distribution for every $t\geq 0$. Wishart processes were introduced in the ’90s by Bru and have become a popular choice for modeling stochastic covariance. For example, Wishart processes are used in multi-dimensional Heston models to describe the instantaneous volatility of multiple assets. Models for energy and interest rate markets involve stochastic \emph{partial} differential equations, and thus call for infinite-dimensional covariance models. In our work, we introduce and analyze infinite-dimensional Wishart processes, and discuss some of their advantages and shortcomings.
Math Seminar: Central limit theorems in deterministic dynamical systems
Dr. Dalibor Volny
Monday, October 2, 2023
11:20 AM – 12:20 PM
BSB 108
We deal with central limit theorems in dynamical systems, i.e. for strictly stationary sequences of random variables. Methods that have been used work in dynamical systems of positive entropy only. By Burton and Denker, later by Volny (functional CLT) it has been proved that in any ergodic and aperioadic dynamical system, a CLT with convergence to a normal law (Brownian motion, in the functional case) exists. Here we deal with convergence towards stable laws (stable processes). The results are due to Zemer Kosloff and Dalibor Volny.
Math Seminar: The Cauchy-Riemann Equations on Hartogs Triangles
Dr. Mei-Chi Shaw, University of Notre Dame
Friday, April 28, 2023
11AM – 12PM
BSB 132
Also available on Zoom: https://tinyurl.com/9nrnveur
The Hartogs triangle in the complex Euclidean space is an important example in several complex variables. It is a bounded pseudoconvex domain with non-Lipschitz boundary. In this talk, we discuss the extendability of Sobolev spaces on the Hartogs triangle and show that the weak and strong maximal extensions of the Cauchy-Riemann operator agree (joint work with A. Burchard, J. Flynn and G. Lu). These results are related to the Dolbeault cohomology groups with Sobolev coefficients on the complement of the Hartogs triangle. We will also discuss some recent progress for the Cauchy-Riemann equations on Hartogs triangles in the complex projective space (joint work with C. Laurent- Thiébaut).
This seminar is held at Rutgers-Camden, as part of a joint seminar with the Complex Analysis and Geometry seminar at Rutgers-New Brunswick.
Math Seminar: Metropolized Hamiltonian Monte Carlo on highdimensional Gaussian Targets
Dr. Stefan Oberdörster, University of Bonn, Germany
Friday, March 24, 2023
12-1 PM in BSB132
In this talk, we will discuss recent developments regarding the convergence of Metropolis-adjusted Hamiltonian Monte Carlo on Gaussian target distributions. These targets stand out amongst the strongly log-concave distributions due to their analytical feasibility. Based on coupling techniques, we show contractivity in a specially designed Wasserstein distance. This yields upper mixing time bounds with respect to total variation that are dimensionally tight for cold start by a conductance argument.
Joint work with Nawaf Bou-Rabee (Rutgers) and Andreas Eberle (Bonn).
Math Seminar: Principled Mathematical Models for the Spotted Lanternfly Invasion
Dr. Benjamin Seibold, Temple University
Friday, February 17, 2023
12-1 PM in BSB132
Also available on Zoom: https://tinyurl.com/9nrnveur
The spotted lanternfly is an invasive species that is spreading in the Eastern United States. Introduced in 2014 to Eastern Pennsylvania, it has since spread within PA and to several adjacent states. Due to its ability to severely compromise lumber, grape, and crop production, it has been called “the worst invasive species to establish in the US in a century.” In this presentation we showcase our team’s efforts to produce principled models for the lanternfly life cycle and its dependence on climatic conditions, with the goal to generate quantitatively accurate predictions of the pest’s establishment potential across the country. In addition to intriguing mathematical models and challenging cross-disciplinary efforts on properly calibrating the models, this research also induces an intriguing need for specialized moving mesh methods. We showcase how biological properties like diapause manifest in a characteristic rank-1 structure of the population evolution operator, and highlight predictions on the pest’s future establishment, including how humans facilitate its spread.
Math Seminar: Weighted L² -estimates for ∂ and its applications
Dr. Song-Ying Li, University of California, Irvine
Friday, October 28th, 2022
11:30 AM – BSB116
Also available on Zoom: https://tinyurl.com/9nrnveur
Abstract: In this talk, I will introduce the Hörmander’s weighted L² estimates for Cauchy-Riemann operator and then present some applications which includes sharp pointwise estimate and uniform estimate for the canonical solution for Cauchy-Riemann equation ∂u = f on a classical bounded symmetric domain in Cn and productive domains. The second application is my recent work on applying the weighted L2 estimates to study the Corona problem in several complex variables.
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