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.

Asymptotic bounds on the d-invariant (Joint with Santana Afton and Tye Lidman).

In preparation.

Topological symmetry groups of algebraically trivial theta graphs (Joint with Allison Moore).

In preparation.

A link concordance group from knots in connected sums of S^2 x S^1 (Joint with Matthew Hedden).

In preparation.

A study of two-periodic weft-knitted textiles using the theory of knots and links (Joint with Shashank Markande, Sabetta Matsumoto, and Sarah Pritchard).

Preprint.

A note on String Link Concordance and Pure Braids. arXiv:2009.04641.

Accepted.

An Analogue of Milnor's Invariants for Knots in 3-Manifolds. Accepted for publication by Algebraic and Geometric Topology. arXiv:1910.12108.

Collaborators (past and present):

Research Advising:

Summer 2020

Madison Ford (Wayne State University, Detroit, MI), Benjamin Pagano (Occidental College, Los Angeles, CA), Sarah Pritchard (Georgia Tech, Atlanta, GA), 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.

Fall 2020

Erin and Sarah 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.

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

Spring 2022

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

Summer 2022-

Sarah is working on a senior thesis on knot theory applied to knitted materials co-advised by Sabetta Matsumoto and myself.

Research Students:

Graham Lewis (Spring 2022)

Sarah Pritchard (Summer 2020, Fall 2020, Senior Thesis Advising Spring 2022-Present)

Erin Wilkerson (Summer 2020, Fall 2020)

Madison Ford (Summer 2020)

Invited Talks:

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.

Recent Conferences Attended:

April 25-29, 2022

Braids in Low-Dimensional Topology, ICERM, Providence, RI

April 6-9, 2022

Joint Mathematics Meetings 2022 (Online)

March 21-25, 2022

Braids in Symplectic and Algebraic Geometry, ICERM, Providence, RI

February 14-18, 2022

Braids in Representation Theory and Algebraic Combinatorics, ICERM, Providence, RI

December 10-12, 2021

Tech Topology Conference (Organizer) (Online)

July 26-30, 2021

Tech Topology Summer School on 4-Manifolds (Organizer)

April 2021

Nearly Carbon Neutral Geometric Topology Conference

April 23-26, 2021

paraDIGMS Spring Conference: Diversity in Graduate Mathematical Sciences (Online), AMS + IMSI

March 13-14, 2021

AMS Southeastern Sectional Meeting (special session organizer) (Online), Georgia Tech, Atlanta, GA

March 7, 2021

Math For All Conference, New Orleans, LA

January 11-15, 2021

Floer homology in low-dimensional topology (Online), Simons Center for Geometry and Physics, Stonybrook, NY

December 4-6, 2020

Tech Topology Conference (Organizer) (Online)

November 20-23, 2020

paraDIGMS Fall Conference: Diversity in Graduate Mathematical Sciences (Online), AMS + IMSI

Sep 17-20, 2020

BIRS-CMO workshop on Topological Complexity and Motion Planning (Online)

June 7-12, 2020

BIRS Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4 (Online)

December 6-8, 2019

Tech Topology Conference (Organizer)

June 10-14, 2019

LG&TBQ, University of Michigan, Ann Arbor, MI.

June 3-7, 2019

Smooth concordance classes of topologically slice knots, American Institute of Mathematics, San Jose, CA,

March 15-17, 2019

AMS Sectional at Auburn University, Auburn, AL.

Dec. 12-14, 2018

Virginia Topology Conference at University of Virginia, Charlottesville, VA.

July 11 - 15, 2018

The topology and geometry of low dimensional manifolds: a celebration of the mathematics of Bob Gompf at at the University of Texas at Austin, Austin, TX

June 25 - 19, 2018

Topology in Dimensions 3, 3.5, and 4 at the University of California, Berkeley, CA.

Feb. 12 - 16, 2018

Knotted embeddings in dimensions 3 and 4 at the Centre International de Rencontres Scientifiques in Luminy, Marseille, France.

Jan. 12 - 13, 2018

Joint Mathematics Meetings at the San Diego Convention Center, San Diego, CA.

Nov. 17 - 19, 2017

58th meeting of the Texas Geometry and Topology Conference at the University of Texas at Austin, Austin, TX.

Nov. 10 - 12, 2017

Lloyd Roeling Mathematics Conference at The University of Louisiana at Lafayette, Lafayette, LA

July 30 - Aug. 4, 2017

CMO-BIRS Thirty Years of Floer Theory for 3-Manifolds at Casa Matematica Oaxaca, Oaxaca City, Oaxaca, Mexico

May 22 - June 2, 2017

2017 Georgia International Topology Conference at the University of Georgia, Athens, GA.

Nov. 12 - 13, 2016

AMS Fall Southeastern Sectional Meeting at North Carolina State University, Raleigh, NC .

Oct. 17 - 21, 2016

Conference on 4-manifolds and knot concordance at Max Planck Institute for Mathematics, Bonn, Germany.

June 6-10, 2016

Perspectives in topology and geometry of 4-manifolds at Inter University Center, Dubrovnik, Croatia.

June 1 - 4, 2016

Topology in dimension 3.5: A conference in memory of Tim Cochran at Rice University, Houston, TX.

Aug. 25 - 29, 2015

The 11th William Rowan Hamilton Geometry and Topology Workshop at Trinity College, Dublin, Ireland.

June 15 - 19, 2015

Princeton Low-Dimensional Topology Workshop at Princeton University, Princeton NJ.

May 18 - 21, 2015

Moab Topology Conference at the Utah State University Regional Campus, Moab, UT.

Apr. 3 - 5, 2015

Redbud Topology Conference at Oklahoma State University, Stillwater, OK.

Jan. 23 - 25, 2015

Invited Graduate Student Panelist at the Nebraska Conference for Undergraduate Women in Mathematics at the University of Nebraska-Lincoln, Lincoln, NE.

Jan. 6 - 9, 2015

Knot Theory and Its Applications to Physics and Quantum Computing at the University of Texas at Dallas, Richardson, TX.

Nov. 18 - 22, 2014

Texas Geometry and Topology Conference at the University of Texas at Austin, Austin, TX.

Aug. 18 - 22, 2014

Graduate Workshop on 4-Manifolds at the Simons Center at Stony Brook University, Stony Brook, NY.

Aug. 4 - 8, 2014

Combinatorial Link Homology Theories, Braids, and Contact Geometry at ICERM at Brown University, Providence, RI.

Jun. 9 - 13, 2014

Topology Students Workshop at the Georgia Institute of Technology, Atlanta, GA.

Apr. 5 - 6, 2014

Graduate Student Topology and Geometry Conference at the University of Texas at Austin, Austin, TX.