2019/2020 Department of Mathematics Events

 Tues, October 1
 4:00 pm

Algebra Seminar
"Strong d-ideals"
Alexandra Milbrand
Located - SE 215

Tues, October 29
4:00 pm

SE 215

Algebra Seminar:  Matthew Toeniskoetter, Visiting Assistant Professor of Mathematics, Harriet L. Wilkes Honors College
Title : Finitely Supported Ideals in Regular Local Rings
Abstract :  We will discuss Zariski's classical theorem on the unique factorization of integrally closed m-primary ideals in 2-dimensional regular local rings and how it breaks down in higher dimensions, then we will describe a partial generalization given by Lipman for a special class of ideals called the finitely supported ideals.

Math Bootcamp
Monday through Thursday
Located - SE 150

Graduate Student Seminar Schedule
A series of short talks (30-60 minutes) which are given with the intended audience of FAU graduate and advanced undergraduate students.

Thurs. October 31

11:00 am

SE 215

Analysis and Application Seminar: Dr. Hidehiko Inagaki, Max Planck Florida Institute of Neuroscience 

Title: Discrete attractor dynamics underlying short-term memory in the frontal cortex
Abstract: Short-term memory, the ability to maintain information over times of seconds, is one of the most fundamental functions of the brain. Neurons in the frontal cortex show persistent changes in spiking activities during memory maintenance and these changes are neural correlates of short-term memories. Interestingly, individual neurons in the brain are essentially memory-less: they can maintain information only for tens of milliseconds. Thus, short-term memory is an emergent property of neuronal networks. A variety of theoretical models have been proposed to resolve this gap in time scales between individual neurons and neuronal networks, yet the mechanisms of short-term memory remain unsolved. We systematically investigated the mechanism underlying persistent spiking activity in mouse frontal cortex, combining intracellular and extracellular electrophysiology with optogenetic perturbations and network modeling. Our results support a model in which discrete attractor dynamics underlie short-term memory.

The SIAM Student Chapter will host and provide refreshments!  

 Sat, November 2
 8:00 am - 5:00 pm

Data Science and Analytics Conference
Office Depot Center, FAU

Mon, November 4

10:00 am

SE 215

MS Presentation:  Dominic Gold, Florida Atlantic University

Title: Possible Applications of TDA Techniques to Digital Image Authentication

Abstract: We will use the technique of persistent homology from the field of topological data analysis. This tool allows us to analyze data on a point cloud and identity unique features of said cloud that persist across multiple levels of "connectedness." Such features include any clusters, holes, and voids created by connecting and filling in the space between -close points, where   is allowed to vary. In that manner, we can see precisely when certain features are "born" and whether or not they "die" or persist. As persistent homology is robust to perturbations of the input data and provides a compact description of said input, it is appealing to believe that one may even analyze encrypted data with it. This presentation will include explicit examples of the calculations done on simplicial complices, the main structure that persistent homology apples too. However, the setting may be also transferred to that of a cubical complex, which is helpful in analyzing digital images if we treat each pixel like a point, identified by its RBG value. 

Tue, November 12

4:00 pm

SE 215

Dr. Lee Klingler, Florida Altaintic University

Title: Semi-clean Group Rings

Abstract:  Let R be a commutative ring.  We call R a clean ring if every element of R can be written as the sum of a unit and an idempotent.  The notion of a clean ring was originally defined by Nicholson [1977] in a study of exchange rings and lifting of idempotents.  Ye [2003] introduced the notion of semi-clean rings:  R is called a semi-clean ring if every element of R can be written as the sum of a unit and a periodic element, where r is called periodic if there are natural numbers k < n such that a^k = a^n.  In joint work (in progress) with Warren McGovern, we attempt to determine necessary and sufficient conditions on a discrete valuation ring R and a finite abelian group G that the group ring R[G] be semi-clean.

Fri, November 15

10:00 am

SE 215

MS Presentation: John White, Florida Atlantic University

Title: An Examination of the Schrodinger Equation

Abstract: The Schrodinger equation is a linear partial differential equation that describes the energy levels and the wave function of a quantum particle. The discovery of the Schrodinger equation was a vital key in the development of quantum physics. This presentation will examine the derivation of the equation, some solutions, and some examples of the equation in action.

 Fri, November 15

11:00 am

SE 215

PhD Dissertation Defense: Omar Babun Codorniu, Florida Atlantic University; Advisor: Dr. Xiao-Dong Zhang

Title: Characterization of Linear Isometries on Complex Sequence Spaces

Abstract:   A linear operator acting on a Banach space is called an isometry if it preserves the norm of the space. An interesting problem is to determine the form or structure of a linear operator by knowing that it is an isometry. This can be done in some instances.

This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear operators have the form of a permutation of the elements of the sequences in the given space, with each component of each sequence multiplied by a complex number of absolute value 1. 

Fri, November 15

4:00 pm

SE 215

FAU Department of Mathematical Sciencew Coloquium: Dr Joel Rosenfeld, University of South Florida 

Arranged by the FAU student chapters of SIAM and the AMS

Title: Interfacing Occupation Kernels with Dynamic Mode Decomposition for the Analysis of Continuous Time Systems

Abstract: In this presentation, we will demonstrate how to incorporate trajectories as the fundamental unit of data in a reproducing kernel Hilbert space (RKHS) framework. The principle objects of study are occupation kernels, which interact with Liouville operators over RKHSs in much the same way that Liouville operators interact with occupation measures over the Banach space of continuous functions as investigated by Lasserre and his colleagues. The objective of this presentation is to demonstrate how these occupation kernels can be integrated into the kernel-based extended DMD framework initiated by Williams and Rowley to enable the direct DMD analysis of continuous time systems. 

Sat, November 16
 9:00 am - 2:45 pm

AMC Middle School Math Day
Tenth Annual Middle School Math Day - Register Now!
FAU Boca Raton Campus

Mon, November 18

SE 215

5:30 pm

MS Presentation:  Christian Corbett, Florida Atlantic University

Title: p-Extensions

Abstract: We consider extensions of noncommutative rings. We define an extension from R to S to be a left (right) p-extension if every principally generated left (right) ideal of S is generated by an element of R. The p-extension from R to S where R and S are unital commutative rings has been well-studied. We aim to generalize the theory of p-extensions to the noncommutative case.

 January 4 - 7, 2020
 TBA

 January 6 - 8, 2020
 TBA

 January 24 - 25, 2020
 TBA

 Thurs, January 30, 2020
 TBA

 Weds, February 5, 2020
 TBA

 March 9 - 13, 2020
 8:00 am - 5:00 pm

 Sat, March 14, 2020
 TBA