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Research Seminars: Graduate Student Colloquium


Past Graduate Student Colloquium:

Fall 2018

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


September 18

Unknotting the knotty notion of knots (and their finite type invariants)

Robyn Brookstulane University

Abstract: TBA





September 25

The Fisher-KPP equation and traveling waves in biology

SDana FerrantirTulane University

Abstract:

Dana





October 2

The Mathematics of Music

Nathan BedellTulane University

Abstract:

In this talk, I'll explain some of mathematical aspects of music theory. In particular, we will focus on the questions: "Why do we use the 12 notes per octave that we see today on a modern piano keyboard, and not some other collection?" and "Why does most of that music limit itself to certain 5 note (pentatonic) and 7 note (diatonic) subsets of that collection?" respectively. 


Our story starts with the history of tuning in the west -- from Pythagorean and meantone temperaments -- including the extended meantone tunings of the Renaissance era, to our modern system of 12 tone equal temperament, some of the various non-western systems of tuning, and finally, to the experimental temperaments that musicians in the "xenharmonic" community have used in recent years to expand the possibilities of our sonic pallet -- all of which will be illustrated with musical examples.




October 9

Extensions of set partitions

Diego VillamizarTulane University

Abstract:

 

In this talk we will show arithmetical and combinatorial properties of set partitions that have restrictions in the size of their blocks. This was a joint work with Jhon Caicedo, Victor Moll and Jose Ramirez.




October 16

Fractional Brownian Motion: Extensions & Estimation in 1-d, n-d and Beyond

Cooper BonieceTulane University

Abstract:

 

Fractional Brownian motion (fBm), whose origins date back to Kolmogorov, is one of the most celebrated models of scale invariance, and has been used in a wide variety of modeling contexts ranging from hydrology to economics.  In this talk, I will discuss some background related to scale invariance and fBm, introduce two extensions of fBm: tempered fractional Brownian motion (tfBm), and operator fractional Brownian motion (ofBm), and discuss some recent work related to wavelet-based estimation of tfBm (joint work with G. Didier, F. Sabzikar), as well as some preliminary results regarding estimation ofBm in a high-dimensional setting.






October 23

Halloween Colloquium: The Unabomber

Hayden HouserTulane University

Abstract:

 

A brief look into the dark side of mathematics. How did a prominent mathematician devolve into one of the country's most notorious criminals?

 


October 30

Normality of Monomial Ideals

Thai NguyenTulane University

Abstract:

In this talk, I will give an introduction to the concepts of integral closure and normality of rings and ideals and explain why I care about them. Focusing on monomial ideals, I will talk about some approaches to tackle the problem of determining the normality of a monomial ideal provided that some of its ordinary powers are integrally closed. It turns out that there is a surprisingly interesting connection between them and some important objects and problems in convex geometry, graph theory and integer programming.


November 6

Topic: GRAPHS AS REDUCED MODELS FOR DISCRETE FRACTURE NETWORKS

Jaime LopezTulane University

Abstract:

 

Discrete fracture networks (DFNs) can be modeled with computationally expensive numerical schemes. We present the formulation of using a graph as a reduced model for a DFN and pose the inversion problem central to this research. We solve the corresponding equations on the graph representation to obtain breakthrough curves, which closely match those created by the high fidelity model. Our solution finds lumped parameters representing the fracture properties, and is used to reduce the computational time required for particle transport calculations. We present examples of creating these reduced models for DFNs with 500 fractures to illustrate the methodology and optimization scheme used to obtain an improved result over a previous formulation.


November 13

Chudnovsky's Conjecture and Waldschmidt Constant

Sankhaneel BisuiTulane University

Abstract:

A well-studied question in algebraic geometry is :

Given a finite set of points in a projective space, what is the minimal degree of a hypersurface that will pass through the points with a given multiplicity?  To answer this question Chudnovsky gave a Conjecture using the multiplicity. We are going to see the basic facts of the Conjecture. In this aspect, Waldschmidt constant plays an important role. We will see the general version of the conjecture. Waldschmidt constant has some important connection with LPP. So, if time allows we are going to see some.  



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