CSUF Pure Math Seminar

The CSUF Pure Math Seminar is an extension of the Geometry Seminar first established at CSUF in 2007.  It is intended as a venue for talks related to algebra, geometry and topology (broadly interpreted) and to be a place where faculty from many different universities can find a friendly and collaborative atmosphere.

2023 Organizer :

Dr. Tommy Murphy, Associate Professor of Mathematics tmurphy@fullerton.edu

Meeting Time:

The Seminar typically meets Fridays  either 11AM-Noon or 2PM-3PM in MH 480.

Fall 2023 Schedule:

• Friday, September 14, 2:00 pm
  Title: "Knots on surfaaces in the 3-sphere".
  Speaker:  Dr. Matt Rathbun
  Abstract:  We will discuss knots siting on a genus 2 Heegaard surface in the 3-sphere, and introduce a notion of equivalence based on the Goeritz group, the group of isotopy classes of orientation-preserving automorphisms of the manifold that preserve the Heegaard splitting.  We will also present two algebraic obstructions to Goeritz equivalence that are straightforward to compute, and discuss extensions related to Goeritz equivalence in lens spaces.
• Friday, September 22, 11:00 am
  Title: "Fun with FRACTRAN".
  Speaker: Tommy Murphy
  Abstract: FRACTRAN is a universal programming language due to John Conway, which allows any Turing machine/computable function to be described by simply multiplying fractions. I will outline how it works, why it is really fun and useful, and explain joint work with undergraduate students K. Kaushik and  D. Weed developing the theory.
• Friday, September 29, 11:00 am
  Title: "New Relations between Intrinsic and Extrinsic Geometric Quantities"
  Speaker: Bogdan Suceava
  Abstract:  In a work on the geometry of minimal submanifolds written in 1968, S.-S.Chern invited more efforts and reflections to identify relationships between intrinsic and extrinsic curvature invariants of submanifolds in various ambient spaces. After 1993, when Bang-Yen Chen introduced the first of his curvature invariants, namely scal - inf(sec), a lot of work has been done to explore this avenue, which represents an active research area. We will survey some of these results obtained in the last three decades, and conclude our talk with new relationships between intrinsic and extrinsic curvature invariants.
• Friday, October 6, 11:00 am
  Title: " Conjugate Points and Morse Theory in Riemannian Geometry"
  Speaker: Russ Phelan (UC Riverside)
  Abstract:  In this talk geared towards undergraduates, we will touch on the primary object of interest in Riemannian geometry: the Riemannian manifold. We will talk about what kinds of properties and techniques we find interesting about Riemannian manifolds. We will focus on Morse theory: roughly a set of theorems that guarantee we can decompose a manifold into the level sets of some function, and that those level sets have a simple structure that can be deduced from the second derivative at critical points. Morse theory becomes most interesting when applied to otherwise difficult-to-understand objects. A famous example is the space of paths connecting two points on a Riemannian manifold. In this setting, another famous theorem allows us to get the needed second derivative data information about how geodesics (curves that minimize distance) spread from one another on a manifold, and when that rate of spread has a stationary point. The only background needed to enjoy this talk is multivariable calculus and linear algebra and the exposition will aim to show the listener the landscape rather than prove specific results in full detail. 
• Friday, October 13, 11:00 am
  Title: " Alperin's Weight Conjecture and Simplicial Complexes"
  Speaker: Adam Glesser
  Abstract:  We present Alperin's Weight Conjecture, one of the most important conjectures in modern finite group representation theory. Additionally, we will show how it can be reformulated in terms of a simplicial complex, namely chains of certain p-subgroups of a finite group G.
• Friday, October 20, 11:00 am
  Double feature!!
  1st Title: A Characterization of Archimedian Solids
  1st Speaker: David Weed
  2st Abstract:  In studying any family of mathematical objects, a fundamental issue is to understand how one object can ``sit inside" another object in the family, preserving the mathematical structure. We are concerned with convex uniform polyhedra. Two famous families of polyhedra live in this class: the Platonic and Archimedean solids, as well as the prisms and antiprisms. Our main result geometrically characterizes the famed Archimedean solids among the convex uniform polyhedra by studying how they sit inside a regular tetrahedron.
  
  2nd Title: Hopf plumbings and generalized Hopf bandings
  2nd Speaker:  Jordan  Incledon
  2nd Abstract: Fibered links are a special class of links that admit a particular kind of decomposition of the complement of the link into fiber surfaces. Hopf plumbings and generalized Hopf bandings are two operations on fiber surfaces that preserve fiberability. In our efforts to understand generalized Hopf bandings as Hopf plumbings, we found that performing a pair of specific  Hopf plumbings results in the same surface as performing a pair of  specific  generalized Hopf bandings. In this talk, we develop a relation in the mapping class group coming from the way the monodromies change via these two operations.
• Friday, October 27, 2:00 pm
  Title: On Bellamy's Large Tangent Value Problem
  Speaker: Dana Clahane (Fullerton College)
  Abstract: Most people think that trigonometry, being a high school level course, has no unexplored areas with no new results.  These people are wrong.  Several recent explorations have been conducted.  We’ll take a look at some of these developments and focus most of this talk on David Bellamy’s question, open since 1998, on how many positive integers are less than their tangents. This talk will be understandable to anyone who has had a trigonometry course, but it will be slightly more consumable for students who have completed a calculus course. (Joint work with Jake Reeves, Kevin Scully among others.)
• Friday, November 3, 2:00 pm
  Title: Braids, Polynomials, and Hilbert's 13th Problem
  Speaker: Jesse Wolfson (UC Irvine)
  Abstract: There are still completely open fundamental questions about polynomials in one variable. One example is Hilbert's 13th Problem, a conjecture going back long before Hilbert. Indeed, the invention of algebraic topology grew out of an effort to understand how the roots of a polynomial depend on the coefficients. The goal of this talk is to explain part of the circle of ideas surrounding these questions. Along the way, we will encounter some beautiful classical objects - the space of monic, degree d square-free polynomials, algebraic functions, lines on cubic surfaces, level structures on Jacobians, braid groups, Galois groups, and configurationspaces - all intimately related to each other, all with mysteries still to reveal. This is ongoing joint work with Benson Farb and with Benson Farb and Mark Kisin
• Friday, November 10
  Speaker: TBA
• Friday, November 17, 11:00 am
  Title:  What can chicken nuggets tell us about symmetric functions, positive polynomials, random norms, and AF algebras?
  Speaker: Stephen Garcia (Pomona College)
  Abstract: A simple question about chicken nuggets connects everything from analysis and combinatorics to probability theory and computer-aided design.  With tools from complex, harmonic, and functional analysis, probability theory, algebraic combinatorics, and computer-aided design, we answer many asymptotic questions about factorization lengths in numerical semigroups.  Our results yield uncannily accurate predictions, along with unexpected results about symmetric functions, trace polynomials, and the statistical properties of certain AF ^C*-algebras.
• Friday, December 1
  Title:  Thickness of Cantor Sets and Applications to Discrete Schrödinger Operators with Sturmian Potential
  Speaker: Alexandro Luna  (UCI)
  Abstract: We give the basics of one-dimensional Cantor set constructions, how they arise in hyperbolic systems, and how to estimate their Hausdorff dimension via thickness. These techniques are applicable in obtaining results concerning Hausdorff dimension of the spectrum of certain Discrete Schrödinger Operators. 

 

Fall 2022 Schedule:

• Friday, October 7, 10:00 am
  Title: "Quadrature of Cubic Segments".
  Speaker:  Dr. Tommy Murphy
  Abstract:  This will be a talk accessible to all undergraduates. In a great triumph of Greek mathematics,  Archimedes showed how to find the area of the region bounded between a parabola and a line,2000 years before calculus was invented. In joint work with M. Rathbun, we extend this to regions bounded between a cubic and a line. The proofs use only elementary calculus and trigonometry.
• Friday, October 13, 3:00 pm
  Title: "Topology of the mapping class group".
  Speaker: Tatsunari Watanabe 
  Abstract: I n this talk, I will introduce the mapping class group of an oriented topological surface and its intrinsic geometric/topological property used in the study of integer solutions of polynomial equations.  The basic background topics including algebraic curves, fundamental groups, and symplectic representation will be briefly introduced. 
• Friday, October 21, 10:00 am
  Title: "Distortion on Cartography".
  Speaker:  Dr. Tommy Murphy
  Abstract:  Differential geometry originally arose when Gauss was hired by King George III (who also ruled Hannover in Germany) to accurately map his Kingdom. I will explain some simple maps of Planet Earth and why constructing accurate maps is still a major problem today. The talk will be accessible to students .

 

Spring 2022 Schedule:

Friday, February 18, 9:00 am	Simona Nistor, from University Al. I. Cuza Ia¸si
Friday, February 25, 9:00 am	Martha Dussan Angulo, Universidade de Sao Paulo, Brazil
Friday, March 4, 9:00 am	Oliver Dragicevic, University of Ljubljana, Slovenia
Friday, March 18, 9:00 am	Vera Tonic, University of Rijeka, Croatia
Friday, March 25, 9:00 am	Baisheng Yan, Michigan State University
Friday, April 1, 9:00 am	Tommy Murphy, California State Univ. Fullerton
Friday, April 22, 9:00 am	Nicoleta Voicu, Transylvania University, Braov, Romania
Friday, May 6, 9:00 am	Mehmet G¨ulbahar, Harran Universitesi, Turkey ¨
Friday, May 13, 9:00 am	Thomas Mark, University of Virginia