Spring 2018
Time & Location: All talks are on Tuesdays in Stanley Thomas 316 at 4:30 PM unless otherwise noted.
Organizer: Alexej Gossmann
January 23
Grad Student Colloquium
A Geometric Complexity Theory Primer
Aram BinghamTulane University
Abstract:
In the words of Scott Aaronson, Geometric Complexity Theory is ``a staggeringly ambitious program for proving P is not equal to NP that throws almost the entire arsenal of modern mathematics at the problem, including geometric invariant theory, plethysms, quantum groups, and Langlands-type correspondences―and that relates the P = NP problem, at least conjecturally, to other questions that mathematicians have been trying to answer for a century.'' We will say as much as we can about this area in 40 minutes or so.
February 6
A Base Case for Proving the Equality of Symbolic and Ordinary Powers of Edge Ideals of Cycles
Joseph SkeltonTulane.University
Abstract:
This talk will present the foundation for the case k=2 as a base case for showing the equality of symbolic and ordinary powers of edge ideals of cycles. The proof itself works off of basic properties of ideals and rings. I will introduce basic definitions and theorems as needed.
February 27
Directed Topology and Dihomotopy Theory
Robyn BrooksTulane University
Abstract:
Directed Topology is a relatively new field of topology that arose in the `90s as a result of the abstraction of homotopy theory. The general aim of this theory is to model non-reversible phenomena. In this talk I will introduce the basics of directed topology and dihomotopy theory, and provide several illustrative examples. Finally, I will discuss a few of the potential tools that may be used to further research in this area.
March 6
Stem Cell Population Growth as an Age-Dependent Branching Process
Hayden HouserTulane University
Abstract:
Biologists studying cell population growth lack an effective way to estimate the probability of stem cell proliferation due to inconsistencies between the experimental and theoretical models. Here we study the asymptotic properties of the age-dependent branching process to gain insight into the long-term behavior of stem cell populations. We then develop a model that assigns a unique range of probabilities to each observed value of population growth, establishing a framework for analyzing similar processes which are dependent on unknown parameters.
March 20
MMD-system, A Finite Combinatorial Approach to Boltzmann Entropy
Sergio VillamarinTulane University
Abstract:
In order to make a finite interpretation to the second law of thermodynamics using Boltzmann entropy, we propose a particular finite mathematical model, a Micro-Macro-Dynamical-System (MMD-system), in which we show a characterization of a perfect entropy MMD-system, showing that in a mathematical context the second law of thermodynamics almost never applies. We also find the average number of MM-systems that have a perfect entropy state by fixing the dynamics, the macro-states or both proving a combinatorial identity. After this we show how to bound the error set of an MM-system and characterize the worst-case scenario for the second law.
April 3
Arithmetic of Elliptic Curves
Vaishavi SharmaTulane University
Abstract:
The theory of elliptic curves is rich, varied, and vast. I will talk about some important properties of these curves and their rational points. We will see a few examples that illustrate the method of infinite descent by Fermat and talk about the Mordell-Weil theorem.
April 17
Topic
Padi FusterTulane university
Abstract:
In this talk I will give an introduction to differential forms and I will try to explain how to use Hodge Theory to rewrite PDE's on manifolds. Also some cute thing about spherical harmonics. It will be mostly tools and classic results on differential topology and algebraic topology and 3 seconds of PDE's.
Date
Inconsistent Mathematics: What If Everything You Knew Were Wrong... and Right... at the Same Time?
Nathan BedellTulane University
Abstract:
In this talk, I'll give a brief overview of some of the classic paradoxes that have arisen both in philosophy and mathematics, and then discuss some of the more unorthodox approaches to the resolution of these paradoxes: Namely, dialetheism, and paraconsistent logic -- that is, respectively, the philosophical belief in true contradictions, and the sort of mathematical framework that allows us to reason with inconsistencies in a non-trivial way. Time permitting, I'll also discuss some of the recent work of Zach Weber on paraconsistent naive set theory, and how this (and paraconsistent mathematics more generally) potentially relate to Lawvere's theorem and some of my work in graded category theory.
