# 2019/2020 Department of Mathematics Events

 Tues, October 1 4:00 pm Algebra Seminar "Strong d-ideals" Alexandra Milbrand Located - SE 215 Thurs, October 3  11:00 am Analysis and Applications "Average Length of the Longest Path in Acyclic Orientations on Complete Bipartite Graphs" Jessica Khera Located - SE 215 Mon, October 7  4:00 pm Crypto Café "Cryptanalysis of NewHope " Shaun Miller Located - SE 215 Tues, October 294:00 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. October 8 - 31 4:00 pm - 7:00 pm Math Bootcamp Monday through Thursday Located - SE 150 October 11  -  November 22 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 $\varepsilon$-close points, where $\varepsilon$  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 Logical Foundations in Computer Science Wyndham, Deerfield Beach, Florida January 6 - 8, 2020 TBA International Symposium on Artificial Intelligence and Mathematics, 2020 Sonesta Fort Lauderdale, Florida January 24 - 25, 2020 TBA Florida Geogebra Conference Friday Jan 24  - Pompano Beach High SchoolSaturday Jan 25 - Florida Atlantic University Thurs, January 30, 2020 TBA American Mathematics Competition 10/12A Annual AMC Contests for Middle and High School Students FAU Boca Raton Campus Weds, February 5, 2020 TBA American Mathematics Competition 10/12A Annual AMC Contests for Middle and High School Students FAU Boca Raton Campus March 9 - 13, 2020  8:00 am - 5:00 pm Southeastern International Conference on Combinatorics, Computing, and Graph Theory Student Hospitality Center Sat, March 14, 2020 TBA FAU Math Day 16th Annual FAU Math Day FAU Boca Campus