Both speakers are recent recipients of NSF Career Grants for young mathematicians.
(You may sort by room or by time of presentation.)| Time | Room | Title and speaker | Abstract |
|---|---|---|---|
| 12:00-1:20 (Topology) | LBJSC 3-21.3 | Morse Theory on a Point Hiro Lee Tanaka Texas State University | In this talk, we’ll give an introduction to Morse theory – a way to study a manifold using real-valued functions. Along the way we will discover that Morse theory on a point is interesting, and if time allows, we will learn about stacks, sheaves, and associative algebras. |
| 1:30-2:50 (Applied Mathematics) | LBJSC 3-21.3 | The Landau equation does not blow up Nestor Guillen Texas State University | The Landau equation is a (partial) differential equation predicting the statistical distribution of particles in a gas by accounting for transport effects and particle collisions, it is a fundamental object of study in statistical mechanics and one of special interest to plasma physics — i.e. physics describing the surface of the sun, the earth’s ionosphere, or the interior of a Tokamak fusion reactor. In this talk I will provide an introduction to this equation, review its basic features and recent history. I will also describe recent work with Luis Silvestre where we answer the decades-old question of whether the equation has global smooth solutions or whether solutions blow up in finite time. This result is made possible by three things: a “lifting” of the equation that decomposes its nonlinear structure, a hidden rotational structure, and a log-Sobolev inequality for functions on the sphere. Students with interests in analysis and mathematical physics are especially encouraged to attend — some of the ideas for the proof will be described first in the simpler setting of the heat equation. |