I am a fifth year PhD student at SUNY Binghamton ​advised by Cary Malkiewich. I study algebraic ​topology and homotopy theory. Recently I have ​been working on problems in equivariant ​cobordism, homotopical fixed point theory, and ​applications of K-theory to manifolds.

Here is my CV.

Contact Information

Department of Mathematics and Statistics

Binghamton University

PO Box 6000

Binghamton, NY 13902

Office: Whitney 302

Email: lwilli39 at binghamton dot edu

Research

I study algebraic topology and homotopy theory. I am particularly interested in homotopical fixed point theory, equivariant cobordism, and applications of K-theory to manifolds.

Papers and Preprints

Periodic Points and Equivariant Parameterized Cobordism (coming soon)

Older Papers

Orlicz-Sobolev Inequalities and the Dirichlet Problem for Infinitely Degenerate Elliptic Operators

(With Theo Lavier, Usman Hafeez, and Luda Korobenko; Electronic Journal of Differential Equations 2021)

Configuration Spaces for the Working Undergraduate

(Rose Hulman Undergraduate Mathematics Journal 2020)

The Representation Theory of Quantum Groups and Connections to Knot Theory

(Undergraduate Thesis)

Teaching

Fall 2024 (as instructor of record)

• Math 224: Differential Calculus, course website
  
• Math 227: Integral Calculus, course website
  

Past Teaching (all as instructor of record)

• At Binghamton
• Spring 2021
  
• Math 147 Introduction to Statistics
  
• Fall 2020
• Math 147 Introduction to Statistics
  
• At Reed College
  
• Spring 2020
  
• Math 342 General Topology
  
• Fall 2019
  
• Math 141 Introduction to Statistics
  

Conferences/Travel

• 2024
• Ohio State Topology Seminar, December 05 (Upcoming)
  
• Cornell Topology Seminar, November 12 (Upcoming)
  
• University of Virginia Topology Seminar, October 31 (Upcoming)
  
• BUGCAT 2024, October 26-27, SUNY Binghamton (Upcoming)
  
• AMS Eastern Sectional, October 19-20, SUNY Albany (Upcoming)
  
• Collaborative Workshop in K-theory and Scissors Congruence, July 29 - August 02, Vanderbilt University
  
• Algebraic Structures in Topology II, June 5 - 14, San Juan
• GSTGC 2024, April 12 - 14, Michigan State University
• Midatlantic Topology Conference, March 23 - 24, Northeastern University
• 2023
• BUGCAT 2023, November 11 - 12, Binghamton University
  
• Young Topologist Meeting, July 24 - 28, EPFL
• Summer School on Scissors Congruence, Algebraic K-theory, and Trace Methods, June 26 - 30, Indiana ​University
• Midatlatic Topology Conference, April 15 - 16, University of Pennsylvania
• 2022
• BUGCAT 2022, November 5 - 6, Binghamton University
  
• Homotopical Methods in Fixed Point Theory, July 11 - 15, University of Colorado, Boulder
• Union College Mathematics Conference, June 3 - 5, Union College
• 2021
• BUGCAT 2021, November, Online
  
• PCMI Graduate Summer School in Motivic Homotopy Theory, July, Online
• GSTGC, April, Online
• Midwest Topology Seminar, April, Online