Research

The introduction of my thesis contains a summary of some of my research interests for both mathematicians and non-mathematicians, you can find this introduction here.

Publications:

In preparation.
A study of two-periodic weft-knitted textiles using the theory of knots and links (Joint with Shashank Markande, Sabetta Matsumoto, and Stanley Pritchard).
Submitted.
Heegaard Floer homology and the word metric on the Torelli group (Joint with Santana Afton and Tye Lidman). arXiv:2501.11244
Submitted.
A note on String Link Concordance and Pure Braids. arXiv:2009.04641.
In print.
An Analogue of Milnor's Invariants for Knots in 3-Manifolds. Algebraic & Geometric Topology 24.6 (2024): 3043-3067. link.
In preparation.
A link concordance group from knots in connected sums of S^2 x S^1 (Joint with Matthew Hedden).

Other research activities:

I was an organizer for the AIM Research Community on 4-Dimensional Topology in 2021 and I participated in the ICERM semester on Braids as well as SRiM at SLMath/MSRI.

I am also a founding mentor for the Atlanta Undergraduate Research Mathematics Seminar, a joint effort between metro Atlanta Universities.


Research Advising:

Sum 2022-Spr 2023

Stanley Pritchard was co-advised by Sabetta Matsumoto and I on an interdisciplinary project on concordance properties of knitted materials.

Spring 2022

Graham Lewis worked on a solo research project on link surgeries with left orderable fundamental groups mentored by Hannah Turner and myself.

Fall 2020

Erin Wilkerson (Clark Atlanta University, Atlanta, GA) and Stanley Pritchard worked on solo research projects with me related to their REU work. Erin is attending Florida State University starting in Fall 2021 pursuing her Masters in Biomathematics while being fully funded by the Leslie N. Wilson-Delores Assistantship.

Stanley wrote a final report of his work (Milnor's Invariants of Pure 3-Braids) and won 3rd place for his presentation at the GT Undergraduate Research Symposium.

Summer 2020

Madison Ford (Wayne State University, Detroit, MI), Benjamin Pagano (Occidental College, Los Angeles, CA), Stanley Pritchard, and Erin Wilkerson (Clark Atlanta University, Atlanta, GA) did a research project with me through the Georgia Tech Math REU and assisted with admitting students. All research was conducted online due to COVID-19

They wrote up Exploring Solvability of the String Link Concordance Group Using Milnor's Invariants and presented a conference poster.

Invited Talks:

January 2025
Joint Mathematics Meetings, Seattle, WA
April 2024
Geometry Seminar at University of Virginia, Charlottesville, VA
March 2024
Topology Seminar at Oklahoma State University, Stillwater, OK
February 2024
Colloquium at Smith College, Northampton, MA
September 2023
Geometry and Topology Seminar at University of Massachusettes, Amherst, MA
July 2023
Topology of 3- and 4- Dimensional Manifolds Mini-Conference at Princeton University, Princeton, NJ
April 2023
Geometry-Topology Seminar at MIT, Cambridge, MA
April 2023
Topology Seminar at Texas State University, San Marcos, TX
March 2023
Topology Seminar at Dartmouth College, Hanover, NH
November 2022
Geometry and Topology Seminar at Duke University, Durham, NC
October 2022
Topology Seminar at Louisiana State University, Baton Rouge, LA
June 2022
New Developments in Four Dimensions Conference at the University of Victoria, Victoria, BC
April 2022
Joint Mathematics Meetings (Online)
December 2021
Haverford-Bryn Mawr Bi-Co Math Colloquium, Haverford, PA
November 2021
AMS Sectional, Mobile, AL
October 2021
Bard College Colloquium, Annandale-On-Hudson, NY
June 2021
Nearly Carbon Neutral Geometric Topology Conference
April 2021
Topology Seminar at Rice University, Houston, TX
March 2021
CKVK* Seminar at The Ohio State University, Columbus, OH
January 2021
Topology Seminar at UC Riverside, Riverside, CA
December 2020
Tech Topology Conference, Atlanta, GA
October 2020
Boston College Topology, Geometry, and Dynamics seminar, Chestnut Hill, MA
September 2020
Eigen* Undergraduate Colloquium at Andrews University, Berrien Springs, MI
May 2020
HF Reading Seminar at University of Virginia, Charlottesville, VA
April 2020
AMS Sectional (cancelled due to COVID-19) at Purdue University, West Lafayette, IN
March 2020
AMS Sectional (cancelled due to COVID-19) at University of Virginia, Charlottesville, VA
November 2019
Geometry-Topology Seminar at Virginia Commonwealth University, Richmond, VA
November 2019
Research Horizons Seminar at Georgia Tech, Atlanta, GA
October 2019
Topology Seminar at the University of Georgia, Athens, GA
September 2019
Geometry-Topology Seminar at Georgia Tech, Atlanta, GA
July 2019
Mathworks Colloquium at Texas State University, San Marcos, TX
March 2019
AMS Sectional at Auburn University, Auburn, AL
December 2018
Virginia Topology Conference at University of Virginia, Charlottesville, VA
October 2018
Geometry/Topology Seminar at University of California, Davis, CA
October 2018
Colloquium at Sam Houston State University, Huntsville, TX
September 2018
Geometry Topology Seminar at the Georgia Institute of Technology, Atlanta, GA
April 2018
Topology Virtual Seminar at Louisiana State University, Baton Rouge, LA
January 2018
Joint Mathematics Meetings at the San Diego Convention Center, San Diego, CA
November 2017
Lloyd Roeling Mathematics Conference at The University of Louisiana at Lafayette, Lafayette, LA
September 2017
Colloquium at Texas Christian University, Ft. Worth, TX.
September 2017
Topology Seminar at the University of Texas, Austin, TX.
August 2017
CMO-BIRS Thirty Years of Floer Theory for 3-Manifolds, Oaxaca, Mexico.
November 2016
AMS Southeastern Sectional Meeting at North Carolina State University, Raleigh, NC.
October 2016
Hausdorff Institute for Mathematics, Bonn, Germany.
January 2015
Invited graduate student panelist at the Nebraska Conference for Undergraduate Women in Mathematics at The University of Nebraska-Lincoln, Lincoln, NE.

Contact

Email mkuzbary@amherst.edu
Department of Mathematics & Statistics
Amherst College
202 Seeley Mudd Building
31 Quadrangle
Amherst, MA 01002