## Upcoming Events

## February 2020

## Andrew Papanicolaou, NYU, Principal component analysis for implied volatility surfaces

Principal component analysis (PCA) is a useful tool when trying to uncover factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close…

Find out more## Dmitriy Morozov, Persistent Homology: Applications and Computation

Persistent homology is a key method in topological data analysis, a young but rapidly growing field at the intersection of computational geometry and algebraic topology. Persistence is used to describe the shape of data in a way that generalizes clustering:…

Find out more## Paata Ivanisvili, UC Irvine, Bellman function in analysis

Many estimates in analysis have certain “common structures” which makes it possible to obtain them with what is now called Bellman function method. Originally the method appeared in control theory (stochastic or deterministic), however its systematic use in harmonic analysis…

Find out more## December 2020

## Huy Nguyen, Brown University, Mathematical Aspects of Free-boundary Problems in Fluid Mechanics

Free-boundary problems are partial differential equations in which the unknown function and its domain must be simultaneously determined. They arise ubiquitously as mathematical models for phenomena in many fields, most notably in physics, biology and finance. Free boundary problems are…

Find out more## Weilin Li, Courant Institute, Generalization error of minimum weighted norm and kernel interpolation

A central question in machine learning theory is whether an algorithm enjoys good generalization, which is the ability to correctly predict new examples from prior observations. While classical wisdom advocates for methods with fewer parameters than data points in order…

Find out more## Hangjie Ji, UCLA, Dynamics of thin liquid films on vertical cylindrical fibers

Thin liquid films flowing down vertical fibers exhibit complex and interesting interfacial dynamics, including droplet formation and traveling wave patterns. Such dynamics play a crucial role in the design of heat and mass exchangers for many engineering applications, including cooling…

Find out more## Fatma Terzioglu, University of Chicago, Mathematics of some emerging imaging techniques

Computerized tomography techniques, which are used for visualizing the interior structure of an object of interest in a non-invasive manner, have played a central role in medical imaging, industrial non-destructive testing, geophysics, astronomy, and other fields. Yet, the quest for…

Find out more## Yuan Gao, Duke University, From rare events to almost sure events: optimal controlled random walk on point clouds

We focus on analysis and data-driven algorithms for rare events such as essential conformational transitions in biochemical reactions which are modeled by Langevin dynamics on manifolds. We first reinterpret the observed transition paths from the stochastic optimal control viewpoint, which…

Find out more## Raghavendra Venkatraman, Carnegie Mellon University, Interfaces and Defects in Heterogeneous and Anisotropic Media: From Materials Science to Geometric Flows

Energy-driven pattern formation is ubiquitous in nature; the character and dynamics of such patterns is selected as local minimizers and gradient flows, respectively, of non-convex, and often, non-local energies with multiple spatio-temporal scales. Analysis of such patterns sheds valuable insight upon their origins, and from…

Find out more## January 2021

## Sam Hopkins, University of Minnesota, Order Polynomial Product Formulas and Poset Dynamics

Sam Hopkins will present a heuristic for finding special families of partially ordered sets. The heuristic says that the posets with order polynomial product formulas are the same as the posets with good dynamical behavior. Here the order polynomial is…

Find out more## Alexandru Hening, Tufts, A general theory of coexistence for ecological communities

A fundamental problem from population biology is finding conditions under which interacting species coexist or go extinct. I present results that lay the foundation for a general theory of stochastic coexistence. This theory extends and makes rigorous Modern Coexistence Theory…

Find out more## Alexandria Vokening, Northwestern University, Modeling and analysis of zebrafish-skin patterns

Many natural and social phenomena involve individual agents coming together to create group dynamics, whether they are cells in a skin pattern, voters in an election, or pedestrians in a crowded room. Here I will focus on the specific example…

Find out more## Laura Colmenarejo, University of Massachusetts- Amherst, An insertion algorithm on multiset partitions with applications to diagram algebras

In algebraic combinatorics, the Robinson-Schensted-Knuth algorithm is a fundamental correspondence between words and pairs of semistandard tableaux illustrating identities of dimensions of irreducible representations of several groups. In this talk, I will present a generalization of the Robinson-Schensted-Knuth algorithm to the…

Find out more## Andy Manion, USC, Heegaard Floer homology in topology and representation theory

I will give a tour of the origins of Heegaard Floer homology and its applications in topology and representation theory, highlighting recent work that relates Heegaard Floer homology with a tensor product operation for higher representations as well as with…

Find out more## Simone Rossi, UNC Chapel Hill, Mathematical and Computational Modeling of the Heart

Cardiovascular diseases are a major health and economic concern both in the U.S. and worldwide. Although recent breakthroughs in medical treatments for heart diseases have improved patient outcomes, the complex interplay between many interconnected physical phenomena has been a major…

Find out more## Zixuan Cang, UC Irvine, Topological and Geometric Data Analysis Meets Data-driven Biology

Topological and geometric data analysis (TGDA) is a powerful framework for quantitative description and simplification of datasets' shapes. It is especially suitable for modern biological data that are intrinsically complex and high-dimensional. Traditional topological data analysis considers the geometric features…

Find out more## Martin Helmer, Effective Methods in Algebraic Geometry and Applications

At its most basic, algebraic geometry studies algebraic varieties; that is, the solution sets of systems of polynomial equations. In this talk our focus is on developing a concrete understanding of the geometry and topology of varieties and using this…

Find out more## Michelle Chu, University of Illinois Chicago, Virtual properties of 3-manifolds

A virtual property of a 3-manifold is a property satisfied by a finite cover of the 3-manifold. The study of such properties has been at the heart of several major developments in 3-manifold topology in the past decade. In this talk…

Find out more## Diego Cifuentes, MIT, Advancing scalable, provable optimization methods in semidefinite & polynomial programs

Optimization is a broad area with ramifications in many disciplines, including machine learning, control theory, signal processing, robotics, computer vision, power systems, and quantum information. I will talk about some novel algorithmic and theoretical results in two broad classes of…

Find out more## Anna Weigandt, University of Michigan, Gröbner Geometry of Schubert Polynomials Through Ice

Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as "how many lines meet four fixed lines in three-space?" These problems can be recast as questions about the structure of cohomology rings…

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