Past Graduate Student Colloquium:

**Time & Location**: All talks are on Tuesdays in Stanley Thomas 316 at 4:30 PM unless otherwise noted.

**Organizer**: Alexej Gossmann

January 23

**Aram Bingham**Tulane 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 correspondencesâ€•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

**Joseph Skelton**Tulane.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

**Robyn Brooks**Tulane 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

**Hayden Houser**Tulane 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

**Sergio Villamarin**Tulane 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.

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Date

**Speaker**Institution

**Abstract**: TBA

Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu