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Research Seminars: Graduate Student Colloquium


Fall 2016

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


September 20

Regularity of Powers of Unicyclic Graphs

Selvi BeyarslanTulane University

Abstract:

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September 27

Probabilistic Numerics

Alexej GossmannTulane University

Abstract:

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October 18

Fractional Calculus and Fractional Brownian Motion

Benjamin BonieceTulane University

Abstract:

What does it mean to take 1/2 of a derivative?
Or integrate 2/3 times?  Or, more generally, can we find
a family of operators that `interpolate' the integral and derivative operators?
And what sort of questions can we answer with such tools?

Fractional Brownian motion (fBm) is a generalization of Brownian motion
that allows for correlated increments.  In general, fBm lacks a key property
in stochastic integration theory -- it is not a semimartingale -- and so much
of the machinery from classical theory is unavailable
when considering integration questions related to fBm.


 

 


October 25

Basic Cryptographic Protocols

Ellis FenskeTulane University

Abstract:

In this short talk I will discuss protocols based on public key cryptography, with a brief discussion of the number theory underpinning much of modern asymmetric cryptography and a primary focus on a variety of cryptographic constructs we can design using only public-key cryptography as a building block: signatures, commitments, shuffles, and zero knowledge proofs.

 


November 1

A Simplified Model of Human Birth: Translation of a Rigid Cylinder through a Passive Elastic Tube

Roseanna GossmannTulane University

Abstract:

A simplified numerical model is used to explore the forces on an infant during human birth. Numerical results are compared with the results of a physical model which represents the fetus moving through the birth canal using a rigid cylinder (fetus) that moves at a constant velocity through the center of a passive elastic tube (birth canal). The entire system is immersed in a highly viscous fluid; low Reynolds number allows the Stokes equations to approximate fluid behavior. The pulling force necessary to move the rigid inner cylinder at a constant velocity through the tube is measured, and considered along with the time-evolving behavior of the elastic tube. The discrete tube through which the rigid cylinder passes has macroscopic elasticity matched to the tube used in the physical experiment. The buckling behavior of the elastic tube is explored by varying velocity, length, and diameter of the rigid cylinder, and length of the elastic tube. More complex geometries as well as peristaltic activation of the elastic tube can be added to the model to provide more insight into the relationship between force and velocity during human birth.

 


November 8

Colors of Non-Euclidean Geometry

Sankhaneel Bisui and Sushovan MajhiTulane university

Abstract:

We will eat pizza with Euclidean seasoning and non-Euclidean toppings. We will start with Euclidean postulates and show the transition to the non-Euclidean geometry, especially hyperbolic geometry. Along with various classical models of hyperbolic geometry, we shall touch upon some applications of this strange geometry. We will also present how the physical world is related to geometry, or geometry is related to the physical world... who knows??


November 15

Stochastic Methods in Turbulent Fluids

Nathan Glatt-HoltzTulane University

Abstract:

I will illustrate the many roles that probability and statistics play
in my research concerning turbulent fluid flows.


November 29

Topic: Library Resources for Mathematics Research

Althea Topek and Raquel HorlickTulane University

Abstract:

 

This will be a special information session introducing the elements of the library and those resources of particular interest to mathematics resarchers. Topics will include Interlibrary Loan, graduate study spaces, BibTeX and alternatives, e-books and journals, as well as other research tools such as Browzine and TOC alerts.

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