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Today

Piermarco Cannarsa, University of Rome Tor Vergata, Italy, Propagation of singularities for solutions to Hamilton-Jacobi equations

SAS 1102

The study of the structural properties of the set of points at which the viscosity solution of a first order Hamilton–Jacobi equation fails to be differentiable—in short, the singular set—started with the paper On the Singularities of Viscosity Solutions to Hamilton–Jacobi–Bellman Equations, Indiana Univ. Math. J. 36 (1987), 501–524 by Mete Soner and myself. These…

Arvind Krishna Saibaba, NC State, The Mathematics Behind Imaging

SAS 2102

From x-ray machines to luggage scanners, our lives depend on imaging devices that let us “see” what is impossible to observe with the naked eye. I will explain some of the mathematical ideas that make image reconstructions possible. Along the way, we will solve some fun puzzles that are related to image reconstructions. This talk…

Ella Pavlechko, Visualizing Curves in the Projective Plane

The Italian Renaissance painters began to incorporate perspective into their drawings in the 1400’s, but our eyes naturally understand depth from the 2-dimensional image on the back of our eyeball. It’s this projection on the retina that allows mathematicians to represent field of view with the projective plane, and in this talk we’ll investigate what makes it so difficult to…

Jason Brown, Dalhousie University, Independence Polynomials and Their Roots

Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph G. In addition to encoding useful information about the graph (such as the number of vertices, the number of edges and the independence number), the analytic and algebraic properties can say much about the shape and inter-dependence of…

Sara Maloni Affiliation, University of Virginia, Mapping class group actions on character varieties

In the first part of the talk we will discuss famous topological and dynamical questions and conjectures about character varieties and the associated action of the mapping class group. In the second part of the talk we will discuss joint work with F. Palesi and T. Yang about type-preserving representations of the fundamental group of the three-holed projective…

Cass Miller, UNC, Toward a New Generation of Models to Simulate Two-Fluid Flow in Porous Media

Two fluid flow in porous medium systems is an important application in many different areas of science and engineering.  Overwhelmingly, it is necessary to mathematically model the behavior of applications of concern at an averaged scale where the juxtaposed position of the phases is not resolved in detail.  This length scale is called the macroscale…

Andrew van der Poel, NC State, Reductions & Problems which Computers are Slow to Solve

SAS 2102

We all tackle hard problems everyday, like finding a parking spot in the Dan Allen Deck. However, there are special types of problems which are hard even for a computer to solve. Reductions, conversions of one problem into another, play a critical role in determining the hardness of these computational problems, and lead to philosophical questions…

Teaching and Diversity Statements

An afternoon discussion/workshop by Jo-Ann Cohen on preparing teaching and diversity statements for the job search.  Note unusual time!

Yerkin Kitapbayev, NC State, American Options Pricing Under Stochastic Volatility Models via Picard Iterations

Daniels 371

This paper studies the valuation of American options for a general one-factor stochastic volatility model.  Using the local time-space calculus on surfaces we derive an early exercise premium representation for the option price, parametrized by the optimal exercise surface. The exercise surface is the unique solution to an integral equation of Volterra type. The paper…

Biji Wong, CIRGET, Twisted Mazur Pattern Satellite Knots and Bordered Floer Theory

Bordered Floer theory has proven quite useful for studying satellites. In this talk, I'll discuss how to use gradings in bordered Floer theory to study the Floer thickness, 3-genus, and fiberedness of arbitrarily twisted Mazur pattern satellite knots Q_n(K). We'll show that for all but two satellites, Q_n(K) is not Floer homologically thin, we'll give…

Undergrads Union Grads (UUG) Math Grad School Applications Workshop

SAS 2102

UUG is holding a Math Grad School Applications Workshop. We will have a presentation about applying to grad schools in mathematics. We will touch on the topics of personal statements, CVs, transcripts, GREs, letters of recommendation, and more. The presentation will be followed by a Q&A session with a faculty panel that have all been…

Roman Shvydkoy, University of Illinois, Chicago, Analytical perspectives on the emergence phenomena in systems of collective behavior

Systems governed by laws of self-organization arise in many different contexts including biology (swarming behavior of animals), social (opinion dynamics, social networks),  technological (cosmology, control, robotics), and others.  A particular challenge in studying such systems is to understand how local communication between "agents" gives rise to emergence of global collective behavior characterized by two basic phenomena -- alignment and flocking. In this…

John Nardini, NC State, The Topology of Data

SAS 2102

The 21st century has seen a boom in the production of data as well as methods to analyze data. One such methodology is Topological data analysis (TDA), where concepts from topology are used to infer the patterns underlying data sets. I will provide a basic and accessible introduction to persistent homology, a common type of TDA that is…

Maxim Bichuch, Johns Hopkins University, Robust XVA

We discuss the reasons for the introduction of Valuation Adjustments as a consequence of the financial crisis of 2007-9. We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a defaultable counterparty. The investor does not know the expected rate of return of the counterparty bond, but…

Kornelia Bastin and Johnny Gillings Jr., NC State, News Methodologies and Predicting and Deterring Outbreaks of Malaria (INFORMS presentation)

Daniels 371

Kornelia Bastin, OR PhD Student People are faced with an overwhelming amount of news, only some of which comes from credible sources and is fact verified. The main idea behind this project is to address such issues. The scope of work includes creating an accessible and efficient method for members of the public to get…