Spring 2019
Time & Location: All talks are on Tuesdays in Stanley Thomas 316 at 4:30 PM unless otherwise noted.
Organizer: Robyn Brooks
January 29
Discrete Morse Theory and its Applications in Topological Data Analysis (TDA)
Sushovan MajhiTulane 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.
February 5
SOME COMBINATORIAL IDENTITIES INVOLVING A FAMILY OF GENERALIZED EULERIAN NUMBERS AND POLYNOMIALS
Villamarin Gomez, Sergio NicolasTulane 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.
February 19
Resurgence number and Fiber Product of Projective Schemes
Sankhaneel BisuiTulane University
Abstract:
I am going to present our joint work with Dr. Tai Huy Ha, Dr. A.V. Jayanthan and Abu C. Thomas. Our interest is to investigate the resurgence number of fiber product of projective schemes. In this talk, we will also see how resurgence number corresponding to the ideal of the fiber product of the schemes depends on that of the original schemes. While considering the asymptotic resurgence the resurgence number of the fiber product follows a nice relation with the resurgence of the original schemes. We will also see the relationship and we will also see how there is a possibility of the resurgence number becoming arbitrarily large.
February 26
Combinatorics of Feynman diagrams
Diego VillamizarTulane University
Abstract:
We will discuss the combinatorial definition and some properties of Feynman diagrams based on the book "A combinatorial perspective of Quantum field theory" of Karen Yeats. Also, we will show some connections with Stirling numbers.
March 19
p- numbers... WHY?
Vaishavi SharmaTulane University
Abstract:
In this talk, I will start from scratch and introduce the p- numbers and discuss the field Qp. I'll go over some examples and applications and then finally talk a little about the problems we're working on.
March 26
Towards a dynamic theory of ontologies
Nathan BedellTulane University
Abstract:
In this talk, I will introduce the notion of an "Olog" (short for ontology log), as popularized by David Spivak in his book "Category Theory for the Sciences". An Olog is a natural format for knowledge representation given (usually) by a free category generated by a directed graph, quotiented by some domain-specific relationships expressed as equalities between morphisms in the category. A functor from this category to some other category is interpreted as an implementation, or model of the Olog. I then discuss some of the latest findings in my theory of graded categories, and discuss how this framework might prove useful in extending Spivak's Ologs to a "dynamic" theory of ontologies, what I am tentatively calling a theory of "meta-ontologies", with an eye towards applications in both metamathematics and artificial intelligence, as well as potentially in fields such as biology, psychology, and the social sciences, where a study of such "dynamic ontologies" might yield interesting results which would not otherwise be obvious.
April 2
Have you ever heard of symplectic geometry and contact geometry?
Padi FusterTulane University
Abstract:
In this talk we will give an introduction to symplectic geometry and contact geometry and its relation with classical mechanics. Do not worry, I am sure you have already encountered symplectic manifolds...do you remember the phase space when you were in that ODE's class? Aha! There you have one!
There is a Frobenius Theorem for differential forms? There is a theorem that gives a relation between symplectic geometry and Morse Theory? Whuat?! I am excited!
April 16
The Historical Development of Algebraic Geometry
Corey WolfeTulane University
Abstract:
Modern algebraic geometry has deviated from its starting intuitive ideas to abstract and complex concepts. Based on the work of Jean Dieudonné, we will examine the historical development of the subject and the roles of key mathematicians. This talk will focus on the following trends: transformations and correspondences, invariants, "infinitely near" points, and extensions of geometric objects. We will also see influences from analysis and topology, and more recently, commutative algebra. With such a large scope, this talk aims only to highlight a few important developments in order to better understand the current complex landscape of algebraic geometry.
April 23
Degree Complexes
Jonathan O'RourkeTulane University
Abstract:
The degree complex of an ideal is a simplicial complex that encodes some invariants of the ideal. I will define degree complexes, discuss their relationship to Castelnuovo-Mumford regularity, and give some results describing certain degree complexes.
