Geometry and Combinatorics

Speaker: Graham Denham (Western)

"Katz's proof of Rota-Heron-Welsh part V"

Time: 15:30

Room: MC 108

Geometry and Combinatorics

Speaker: Taylor Brysiewicz (Western)

"TBD"

Time: 15:30

Room: MC 108

Colloquium

Speaker: Frank Sottile (Texas A&M University)

"Webs and Welschinger signs"

Time: 15:30

Room: MC 107

A 3-dimensional subspace f of real polynomials defines a map f : P^1 -> P^2 whose image is a rational plane curve. It is maximally inflected when all of its flexes are real, equivalently, when its Wronski determinant has only real roots. We associate two a priori distinct signs (\pm 1) to f: the Welschinger invariant of the rational curve and the degree of the Wronski map at f. Extensive computation suggests that these signs coincide. While studying this conjecture we were led to a deeper conjecture: From f, we define a a function W : CP^1 -> CP^1 which encodes some real geometry of f and conjecturally gives an object called a web. We conjecture that known bijections between webs and standard Young tableaux and between tableaux and maximally inflected curves recovers the curve.

This talk will explain this picture with compelling evidence and beautiful pictures. It is joint work with Brazelton, Karp, Le, Levinson, McKean, Peltola, and Speyer.

Algebra Seminar

Speaker: (Western)

"TBD"

Time: 14:30

Room: MC 108

TBD

Colloquium

Speaker: Andy Zucker (Waterloo)

"TBA"

Time: 15:30

Room: MC 107

Colloquium

Speaker: Janusz Adamus (Western)

"Introduction to Arc-analytic Geometry."

Time: 15:30

Room: MC 107

Abstract: Arc-analytic geometry is a fairly new branch of real analytic and algebraic geometry, inspired by John Nash's questions about the role of arcs in geometry. It studies the so-called arc-analytic functions and arc symmetric sets. In the algebraic setting, it provides the most satisfactory real counterpart of Zariski topology over an algebraically closed field. In the analytic setting, in contrast, it consists at present mostly of tough open problems. I will give a brief history of the subject with an overview of classical results from the late 80's and the 90's, and discuss both the recent progress and questions. The talk should be accessible to senior math undergrads.

Colloquium

Speaker: Junping Shi (College of William & Mary, VG, USA)

"Reaction-diffusion models for animal movement with spatial memory and nonlocal advection"

Time: 15:30

Room: MC 107

Animal populations often self-organize into territorial structure from movements and interactions of individual animals. Spatial memory is one of cognitive processes that may affect the movement and navigation of the animals. We will review several mathematical approaches of animal spatial movements: (i) reaction-diffusion-advection model with time-delayed memory-based movement; and (ii) reaction-diffusion-advection model with a non-local advection term driven by a cognitive map representing memory of past animal locations embedded in the environment. The well-posedness of models and bifurcation of spatiotemporal patterns will be discussed.

Department Meeting

Speaker:

"location TBA"

Time: 15:30

Room: MC 108