This Week's Seminars and Colloquia

Polynomials over real valued fields and other stuff about hyperfields

Series
Algebra Seminar
Time
Monday, April 6, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Trevor GunnGeorgia Tech

The main goal of this talk is to discuss my proof of a multiplicity formula for polynomials over a real valued field. I also want to talk about some of the raisons d’être for hyperfields and polynomials over hyperfields. This talk is based on my paper “A Newton Polygon Rule for Formally-Real Valued Fields and Multiplicities over the Signed Tropical Hyperfield” which is in turn based on a paper of Matt Baker and Oliver Lorscheid “Descartes' rule of signs, Newton polygons, and polynomials over hyperfields.”

The talk will be held online via Bluejeans. Use the following link to join the meeting.

CANCELLED - - Tiny Giants - Mathematics Looks at Zooplankton

Series
Mathematical Biology Seminar
Time
Wednesday, April 8, 2020 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter HinowUniversity of Wisconsin-Milwaukee

Zooplankton is an immensely numerous and diverse group of organisms occupying every corner of the oceans, seas and freshwater bodies on the planet. They form a crucial link between autotrophic phytoplankton and higher trophic levels such as crustaceans, molluscs, fish, and marine mammals. Changing environmental conditions such as rising water temperatures, salinities, and decreasing pH values currently create monumental challenges to their well-being.

A signi cant subgroup of zooplankton are crustaceans of sizes between 1 and 10 mm. Despite their small size, they have extremely acute senses that allow them to navigate their surroundings, escape predators, find food and mate. In a series of joint works with Rudi Strickler (Department of Biological Sciences, University of Wisconsin - Milwaukee) we have investigated various behaviors of crustacean zooplankton. These include the visualization of the feeding current of the copepod Leptodiaptomus sicilis, the introduction of the "ecological temperature" as a descriptor of the swimming behavior of the water flea Daphnia pulicaria and the communication by sex pheromones in the copepod Temora longicornis. The tools required for the studies stem from optics, ecology, dynamical systems, statistical physics, computational fluid dynamics, and computational neuroscience.

TBA by Vlad Yaskin

Series
Analysis Seminar
Time
Wednesday, April 8, 2020 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vlad YaskinUniversity of Alberta

Tba

The Jones polynomial via quantum group representations

Series
Geometry Topology Student Seminar
Time
Wednesday, April 8, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Tao YuGeorgia Tech

Continuing the theme of Hopf algebras, we will discuss a recipe by Reshetikhin and Turaev for link invariants using representations of quantum groups, which are non-commutative, non-cocommutative Hopf algebras. In the simplest case with the spin 1/2 representation of quantum sl2, we recover the Kauffman bracket and the Jones polynomial when combined with writhe. Time permitting, we will also talk about colored Jones polynomials and connections to 3-manifold invariants.

Anti-Ramsey number of edge-disjoint rainbow spanning trees

Series
Graph Theory Seminar
Time
Thursday, April 9, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zhiyu WangUniversity of South Carolina

An edge-colored graph $G$ is called \textit{rainbow} if every edge of $G$ receives a different color. The \textit{anti-Ramsey} number of $t$ edge-disjoint rainbow spanning trees, denoted by $r(n,t)$, is defined as the maximum number of colors in an edge-coloring of $K_n$ containing no $t$ edge-disjoint rainbow spanning trees. Jahanbekam and West [{\em J. Graph Theory, 2016}] conjectured that for any fixed $t$, $r(n,t)=\binom{n-2}{2}+t$ whenever $n\geq 2t+2 \geq 6$. We show their conjecture is true and also determine $r(n,t)$ when $n = 2t+1$. Together with previous results, this gives the anti-Ramsey number of $t$ edge-disjoint rainbow spanning trees for all values of $n$ and $t$. Joint work with Linyuan Lu.

Global eigenvalue distribution of matrices defined by the skew-shift

Series
Math Physics Seminar
Time
Thursday, April 9, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
BlueJeans: https://bluejeans.com/900271747
Speaker
Marius LemmHarvard University

The seminar is held in BlueJeans: https://bluejeans.com/900271747

A central question in ergodic theory is whether sequences obtained by sampling along the orbits of a given dynamical system behave similarly to sequences of i.i.d. random variables. Here we consider this question from a spectral-theoretic perspective. Specifically, we study large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift on the 2-torus with irrational frequency. We prove that their global eigenvalue distribution converges to the Wigner semicircle law, a hallmark of random matrix statistics, which evidences the quasi-random nature of the skew-shift dynamics. This is joint work with Arka Adhikari and Horng-Tzer Yau.