Undergraduate Colloquium Archive

Spring 2020

Date Speaker Title Abstract
January 27th Jo Nelson
Rice University
Contact encounters in the third dimension Contact geometry is the study of certain geometric structures on odd dimensional differentiable manifolds, which originated in classical mechanics. Manifolds generalize the notion of curves (1 dimensional) and surfaces (2 dimensional) to higher dimensions, though for this talk we will stick to dimension three. A contact structure is a two dimensional subspace which satisfies a maximum non-degeneracy condition which mandates that there be no two dimensional subsurface which is tangent to the contact structure. It also gives rise to a canonically defined vector field, called the Reeb vector field. I will give an introduction to three dimensional differential and contact geometry, primarily focusing on R3and S3as examples,with numerous pictures and animations.
February 17th Michael Norton
KIPP Texas Public Schools
Today's Student Experience in K-12 Math Classrooms I will discuss the challenges and opportunities faced by K-12 math educators in 2020. There are many strategies, protocols, and products that are divined on paper as ideal pedagogical solutions, but then must come alive in a messy reality. Findout about the key components that make for great math teaching & learning, and discover and experience how practitioners -both individual teachers & at those at various levels of the industry -are creating today's student experience in light of (e.g.) the Common Core, the emergence of new digital tools, and the abundance of educational data
March 30th Cabral Balreira
Trinity University
April 13th Junehyuk Jung
Texas A&M University
Tiling the set of integers
April 20th Allison Miller
Rice University

Fall 2019

Date Speaker Title Abstract

Tuesday, September 3rd

*Special day due to Labor Day holiday

Robert Hardt
Rice University
Energy-Minimizing Unit Vector Fields in Three Space

Given a smooth real-valued function g on the unit sphere S in R3, the function u on the closed unit ball B which coincides with g on S and has least energy|𝐷𝑢|2𝑑𝑥𝐵is a harmonic function. These show up in classical mathematics, physics, and many applications; e.g. u represents the longtime steady-state temperature distribution resulting from keeping the surface temperature equal to g. Later,many other interestingproblems required changing real-valued functions to unitvectorfields. This seemingly small change led to many new problems and results. We will look at some of the basic examples, questions and solutions including:

  1. Isthere always aminimizer? Is it always unique? Always continuous?(yes,no,no)
  2. What is the minimizing unit vectorfield u on B such that u(x) = x for x in S? (x/|x|)
  3. Can minimizers have isolated singularities of any degree? (no)
  4. Can minimizers have 1 dimensional singularities (as seen in some liquid crystals)? (no)
  5. Open problems?
September 23rd Siran Li
Rice University
The Many Facets of Harmonic Functions In this talk, we shall describe harmonic functions on a domain in Rnfrom many different aspects ---the mean value properties, the PDEs (partial differential equations), the Newtonianpotential, and the probabilistic perspectives. The regularity theory of harmonic functions will be surveyed. Finally, we will discuss some recent constructions of ''weird'' spaces (manifolds) on which the regularity theory blatantly fails, in stark contrast to the Euclidean case. [Our talk is complimentary to Prof. Bob Hardt's talk at the beginning of the semester.]
October 28th Selim Sukhtaiev
Rice University
Anderson localization for disordered quantum graphs Disorder is one of the central topics in modern science. In this talk, we will discuss a mathematical treatment of a particular disordered system modeling localization of waves in random media. The model in equation was introduced by P. W. Anderson in his Nobel prize winning work in physics which led to a rich mathematical theory of random Schrodinger operators. The present talk is devoted to a particular Anderson model arising in the study of quantum graphs. I will provide an elementary introduction to quantum graphs and mathematical theory of Anderson localization, which lies at the interface of dynamical systems, differential equations, and linear algebra. No previous knowledge of or familiarity with this subject will be assumed
November 18th Alan Reid
Rice University
Q&A for Math Majors and Minors with the Math Department Chair Dr.Reid will begin by talking about some of his mathematical interests, his background, being chair of the department, and how this impacts the lives of undergraduate students. There will be a Q&A session to end the discussion

Spring 2019

Date Speaker Title
January 14th Greg Chambers
Rice University
Constructing homotopies of low complexity
February 18th Jack Petok
Rice University
Densest Sphere Packings, Lattices, and Theta Functions
March 25th Daniel Hast
Rice University
The geometry of redistricting and gerrmandering
April 8th Jen Berg
Rice University
Rental Harmony or, How to use math to make your roommates envy-free

Fall 2018

Date Speaker Title
August 24th Michael Wolf
Rice University
Geometric optimization: An exploration through soap films
September 21st Anastassia Etopolski
Rice University
The Congruent Number Problem and Elliptic Curves
November 9th Max Lieblich
University of Washington
Algebraic geometry in computer vision
November 16th Jacob Kesten and
Sara Edelman-Muñoz
Rice University
What I did last summer

Spring 2018

Date Speaker Title
January 26th Ronen Mukamel
Rice University
Billiards in Polygons
February 23rd Alan Haynes
University of Houston
Constructibility, Solvability, and Origami
March 23rd Casey Douglas
St. Mary's College (MD) / Rice

Fall 2017

Date Speaker Title
August 25th
September 1st
September 15th
Anthony Várilly-Alvarado
Rice University
Primes in arithmetic progressions
September 29th Changhui Tan
Rice University
The mathematics in continuum mechanics
October 20th
October 27th
Arindam Roy
Rice University
Ford Circles
November 10th Ilya Marchenka '19
Anh Tran '19
Rice University
What I Did Last Summer

Spring 2017

Date Speaker Title
January 20th Stephen Wang
Rice University
Shape Shifting: Things you can and cannot do via cut and paste
February 17th Brian Miceli
Trinity University
Combinatorial Enumeration in Pascal's Triangle
March 3rd Betul Orcan-Ekmekci
Rice University
Beyond Classical Derivatives, Still Using Calculus
March 24th David Krcatovich
Rice University
Planning robot motion using configuration spaces
April 7th Neil Fullarton
Rice University
The lantern relation on a surface

Fall 2016

Date Speaker Title
August 26th Frank Jones
Rice University
ABC's of the heat equation
September 2nd Kyle Kinneberg
Rice University
Conformal maps and circle packings
September 14th (Wednesday at 4:30!) Google An event with Google for math majors (room TBA)
September 23th Betul Orcan-Ekmekci
Rice University
Talk postponed until spring semester
September 30th Richard Shadrach
Rice University
Hamilton's quaternions and how to algebraically roll a ball
October 21st Vu Hoang
Rice University
Mathematics and Tightrope walking
October 27th (Thursday!) William Dunham
Bryn Mawr College
Euler in Two Acts
November 4th Zhenghe Zhang
Rice University
Stable and unstable dynamical behaviors in Hamiltonian systems
November 18th Jonathan Celaya '17
Konstantinos Varvarezos '16
Rice University
What I Did Last Summer

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P.O. Box 1892
Houston, TX 77005-1892

Fax (713) 348-5231

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Rice University
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