# Research Seminars: Graduate Student Colloquium

Past Graduate Student Colloquium:

## Spring 2019

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

**Organizer**: Alexej Gossmann

January 29

## Discrete Morse Theory and its Applications in Topological Data Analysis (TDA)

**Sushovan Majhi**Tulane University

**Abstract**:

We eat pizza and talk about Topological Data Analysis (TDA). TDA is an emerging subfield of applied mathematics. Various topological concepts such as homology, persistent homology, discrete Morse theory are becoming widely useful in analyzing and visualizing data. Applications include reconstruction of shapes, 3D printing, feature detection, medical imaging etc. We briefly touch upon Morse theory and its discrete analog. Also, we discuss some of its major applications in TDA.

Date

## SOME COMBINATORIAL IDENTITIES INVOLVING A FAMILY OF GENERALIZED EULERIAN NUMBERS AND POLYNOMIALS

**Villamarin Gomez, Sergio Nicolas**Tulane University

**Abstract**:

The Eulerian polynomials were introduced by Euler when studying the sum of alternating consecutive numbers with a fix exponent. Afterwards he introduced its coefficients as the Eulerian numbers and gave many interesting combinatorial identities, some of which relate to the Riemann Zeta function. In our talk I’ll introduce them and present some of its properties and also some generalizations along with generalizations of the Stirling numbers of the second kind.

Date

## Topic

**Speaker**Institution

**Abstract**: TBA