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Research Seminars: AMS/AWM

Fall 2021

Time & Location: All talks are on Wednesday at 5:00 PM unless otherwise noted.
Organizer: Diaz Morera, Nestor F

 

Wednesday, October 6

Topic: An Introduction to Homogeneous Spaces

Mahir Can | Tulane University

Abstract: In this talk we will explain how two important fields of mathematics, combinatorics, and algebraic geometry, meet. The interplay between the ideas of these two fields lead to remarkable results in representation theory.

Location: Gibson Hall 126A
Zoom Access:
Time:
4:15

 

Wednesday, October 13

Topic: An Illustration of Energy Methods

Kyle K. Zhao | Tulane University

Abstract: Energy methods is an important tool in the study of qualitative properties of partial differential equations. Charlie Doering (Professor of Mathematics and Professor of Physics, University of Michigan - Ann Arbor) once said: "Give me integration by parts and Cauchy-Schwarz inequality, I can conquer the world”. This talk will give an illustration of how these elementary tools could be utilized to prove non-trivial mathematical problems arising in applied science.

Location: Gibson Hall 400A
Zoom Access:  N/A
Time: 4:15

 

Wednesday, October 20

Topic: Divisibility properties of partition numbers

Olivia Beckwith | Tulane University

Abstract: My research focuses on elliptic modular forms and their connections to different areas of number theory. In this talk I will give a short introduction to modular forms, and then I will describe some of my work studying the divisibility properties of numbers which count integer partitions. This includes a discussion of joint work with Scott Ahlgren and Martin Raum, and ongoing joint work with Jack Chen, Maddie Diluia, Oscar Gonzales, and Jamie Su.

Location: Gibson Hall 400A
Zoom Access:  N/A
Time: 4:15

 

Wednesday, October 27

Topic: Statistical Challenges in the Analysis of Methylation Profiles

Michelle Lacey | Tulane University

Abstract: Cytosine methylation is a fundamental epigenetic process that regulates gene expression. Variation in cytosine methylation at CpG dinucleotides is often observed in genomic regions, and a common objective in epigenetic analysis is the detection of differentially methylated sites or regions that may be associated with variation in gene expression related to disease or other factors such as environmental exposure. For sequencing-based methods, this often involves comparing two groups of samples that contain counts of methylated and unmethylated reads, and classical approaches such as logistic regression are typically employed to identify statistically significant differences. However, these algorithms largely ignore sources of both technical and biological bias and variability that violate key statistical assumptions, consequentially producing unreliable results. In particular, our research demonstrates that methylation patterns in individual molecules exhibit strong evidence of local spatial dependence, and further correlation is induced by variability in read coverage in sequencing experiments. This talk will discuss past and present efforts to develop improved statistical models for methylation sequencing data.

Location: Gibson Hall 400A
Zoom Access:  N/A
Time: 4:15

 

Wednesday, November 3

Topic: When Commutative Algebra, Graph Theory and Linear Programming meet

Tai Ha | Tulane University

Abstract: We shall discuss 3 seemingly disjoint sets of problems in commutative algebra, graph theory and linear programming, that turn out to be very closely connected.

Location: Gibson Hall 400A
Zoom Access:  N/A
Time: 4:15

 

Wednesday, November 10

Topic: Linking and knotting in vector fields

Rafal Komendarczyk | Tulane University

Abstract: I will talk about knots and links, their invariants and how they can be applied to problems in fluid dynamics and magnetic relaxation.

Location: Gibson Hall 400A
Zoom Access:  N/A
Time: 4:15

 

Wednesday, November 17

Topic: Landen transformations

Victor Moll | Tulane University

Abstract: The evaluation of the length of an ellipse was one of the interesting problems of the $19^{th}$ century. Landen developed some formulas that lead to the efficient numerical evaluation of these integrals. The talk will include some modern approaches and extensions to this problem.

Location: Gibson Hall 400A
Zoom Access:  N/A
Time: 4:15