## Publications

- On distinct finite covers of 3-manifolds Submitted.

(With Stefan Friedl, JungHwan Park, Bram Petri, and Jean Raimbault) - Linear independence of cables in the knot concordance group. Submitted.

(With Christopher W. Davis and JungHwan Park) - Pretzel links, mutation, and the slice ribbon conjecture. Submitted.

(With Paolo Aceto, Min Hoon Kim, and JungHwan Park) - Concordance of knots in S1xS2. Journal of the LMS (2)98 no. 1, 59-84, 2018.

(With Christopher W. Davis, Matthias Nagel, and JungHwan Park) - 4-dimensional analogues of Dehn's lemma. Journal of the LMS (2)96 no. 1, 111–132, 2017.

(With Daniel Ruberman) - A family of non-split topologically slice links with arbitrarily large slice genus. Proceedings of the AMS 146(1), 439–448, 2018.

(With JungHwan Park) - On the Upsilon invariant and satellite knots. To appear: Mathematische Zeitschrift.

(With Peter Feller and JungHwan Park) - A new family of links topologically, but not smoothly, concordant to the Hopf link.
*Tim Cochran memorial issue, Journal of Knot Theory and its Ramifications*, 26(2): 1740002, 2017.

(With Christopher W. Davis) - Shake slice and shake concordant knots.
*Journal of Topology*, 9(3): 861-888, 2016.

(With Tim D. Cochran) - Satellite operators as group actions on knot concordance.
*Algebraic & Geometric Topology*, 16(2): 945–969, 2016.

(With Christopher W. Davis) - Satellite operators with distinct iterates in knot concordance.
*Proceedings of the AMS,*143(11): 5005-5020, 2015. - Casson towers and filtrations of the knot concordance group.
*Algebraic & Geometric Topology*, 15(2): 1119–1159, 2015. - Injectivity of satellite operators in knot concordance.
*Journal of Topology*, 7(4): 948–964, 2014.

(With Tim D. Cochran and Christopher W. Davis) - Slice knots which bound punctured Klein bottles.
*Algebraic & Geometric Topology*, 13(5): 2713-2731, 2013.

## Miscellaneous

- Research Statement, Teaching Statement, and Diversity Statement
- A short research description
- My PhD thesis (PDF)
- My Erdos number is 4
- In Fall 2016, I participated in the Junior Hausdorff Research Trimester in Topology at the Hausdorff Institute for Mathematics, in Bonn, Germany. We had a conference.
- I gave a 90 second pitch about my research at the Rice Graduate Elevator Pitch Competition; this was meant for a very general audience and as a result, it "has many omissions and contains much that is apocryphal, or at least wildly inaccurate"
- Syllabus for my advanced exam at Rice University
- Errors discovered in Knots and Links by Dale Rolfsen
- Research Statement and Statement of Teaching Philosophy from 2015
- Research Statement and Statement of Teaching Philosophy from 2014

### Seminars/conferences/special sessions co/organized

- EveryTopic Seminar, Fall 2015 and Spring 2016 (co-organized with Carl Wang Erickson), and Spring 2017, (co-organized with McKee Krumpak and Konstantin Matveev)
- AMS Special Session on Women in Topology, Joint Mathematics Meetings, January 2017 (co-organized with Jocelyn Bell (William and Hobart Smith), Eleanor Ollhoff (University of Tennessee), and Candice Price (University of San Diego)
- Conference on 4-manifolds and knot concordance at MPIM, October 2016 (co-organized with Christopher Davis (UW-Eau Claire), Peter Feller (MPIM), Min Hoon Kim (KIAS), Jeffrey Meier (Indiana), Allison Miller (UT Austin), Mark Powell (UQAM), and Peter Teichner (Berkeley/MPIM))
- Spectral Sequences Learning Seminar, Fall 2014
- Heegaard-Floer computationar, Spring 2014
- 4-manifolds seminar, Spring 2014
- Characteristic classes seminar, following Milnor & Stasheff's Characteristic Classes, Summer 2012
- Knot invariants seminar, Summer 2011

## Past and upcoming talks (including some slides)

*4-dimensional analogues of Dehn's lemma*, Georgia International Topology Conference, University of Georgia, May 25, 2017.*Concordance of knots in S1xS2*, AMS Special Session on Invariants of Knots, Links and 3--manifolds (AMS Spring Eastern Sectional Meeting, Hunter College, City University of New York), May 7, 2017.*4-dimensional analogues of Dehn's lemma*, Rice University Topology Seminar, April 17, 2017.*4-dimensional analogues of Dehn's lemma*, UT Austin Topology Seminar, April 12, 2017.*4-dimensional analogues of Dehn's lemma*, Conference on Floer homologies and topology of 4-manifolds, UMass Amherst, April 9, 2017.*4-dimensional analogues of Dehn's lemma*, Notre Dame Topology Seminar, April 4, 2017.*Concordance of knots in S1xS2*, Geometry and Topology seminar, CIRGET (Montreal), March 24, 2017.*Concordance of knots in S1xS2*, Topology Seminar, Brandeis University, March 7, 2017.*Knot theory in dimension 3.5*, Special Colloquium, UC Riverside, February 10, 2017.*Knots, four dimensions, and fractals*, Bowdoin College, February 6, 2017. Slides*4-dimensional analogues of Dehn's lemma,*Joint Mathematics Meetings, January 5, 2017. Slides*Knot theory in dimension 3.5,*UNC Charlotte, December 12, 2016*Knot theory in dimension 3.5,*Hausdorff Center for Mathematics seminar, December 6, 2016.*4-dimensional analogues of Dehn's lemma,*Seminar on knot concordance and 4-manifolds, Hausdorff Institute for Mathematics, September 16, 2016.*Satellite operations and fractal structures on knot concordance,*Topology in dimension 3.5: a conference in memory of Tim Cochran, Rice University, June 2, 2016. Slides*Shake slice and shake concordant knots,*Topology seminar, Indiana University Bloomington, April 28, 2016*Satellite operations and knot concordance,*Colloquium, San Francisco State University, February 18, 2016. Slides*Shake slice and shake concordant knots,*Geometry seminar, University of Virginia, February 9, 2016*Knots, four dimensions, and fractals,*Mathematics Adventures & Diversions, Lafayette College, February 2, 2016. Slides*Is the set of knots a fractal?,*Colloquium, SUNY Geneseo, January 29, 2016. Slides*Shake slice and shake concordant knots,*Joint Mathematics Meetings, January 6, 2016. Slides*Concordance classes of knots and satellite operations,*IGERT seminar, Brandeis University, December 9, 2015*A new family of links topologically, but not smoothly, concordant to the Hopf link,*CMS Winter Meeting, Montreal, QC, December 5, 2015. Slides*Independence of satellite knots in smooth concordance,*AMS Central Sectional Meeting, Loyola University, October 4, 2015*Shake slice and shake concordant knots*, Moab Topology Conference, Utah State University, May 18, 2015*Satellite operators as group actions on knot concordance,*AWM Research Symposium Poster Session, University of Maryland, College Park, April 11, 2015. Poster*Shake slice and shake concordant knots,*EveryTopic Seminar, Brandeis University, March 3, 2015*Shake concordance of knots,*Geometry and Topology Seminar, Syracuse University, October 9, 2014*Satellite operators and knot concordance,*Topology Seminar, Wesleyan University, September 24, 2014*Shake concordance of knots,*AMS Central Sectional Meeting, University of Wisconsin-Eau Claire, September 21 2014*Satellite operators and knot concordance,*Topology Seminar, Brandeis University, September 16, 2014*Satellite operators and knot concordance,*Topology Seminar, Boston College, September 11, 2014*Shake concordance of knots,*Workshop on Topology and Invariants of Smooth 4-manifolds, Simons Center for Geometry and Physics, August 25, 2014*Casson towers and filtrations of the smooth knot concordance group.*PhD Defense, Rice University, April 8, 2014. Slides*Satellite operators on knots, and fractals.*STEM colloquium, University of Wisconsin-Eau Claire, March 7, 2014. Slides*From CFK*Heegaard-Floer computationar, Rice University, April 2, 2014^{-}(K) to CFD^{^}(S^{3}-K).*Calculating the concordance invariant epsilon from Knot Floer homology.*Heegaard-Floer computationar, Rice University, February 19, 2014*An introduction to the concordance invariant epsilon from Knot Floer homology.*RTG Topology Seminar, Rice University, February 14, 2014*The fractal nature of the knot concordance group.*Joint Mathematics Meetings, Baltimore, MD, January 18, 2014. Slides*Satellite operators as group actions on knot concordance.*AMS Central Sectional Meeting, Washington University at St. Louis, October 20, 2013. Slides*Casson towers and filtrations of the smooth knot concordance group.*AMS Central Sectional Meeting, Washington University at St. Louis, October 19, 2013. Slides*A friendly introduction to the philosophy of mathematics.*Current Mathematics Seminar, Rice University, October 10, 2013*Satellite operators with distinct iterates in smooth knot concordance.*Topology Seminar, Rice University, September 9, 2013*Casson towers and filtrations of the smooth knot concordance group.*Topology Seminar, Rice University, August 26, 2013*There exist infinitely many unknotted winding number one satellite operators on knot concordance.*2013 Lehigh University Geometry and Topology Conference, Lehigh University, May 25, 2013. Slides*A friendly introduction to knots in three and four dimensions.*Mathematics Department Colloquium, SUNY Geneseo, April 25, 2013. Slides*A brisk introduction to Legendrian/transverse knots and the slice-Bennequin inequality.*VIGRE Topology Seminar, Rice University, January 29, 2013*Slice knots which bound Klein bottles.*AMS Central Sectional Meeting, University of Akron, October 20, 2012. Slides*Symmetries of knots.*VIGRE Topology Seminar, Rice University, September 21, 2012*Generating functions and random walks.*Current Mathematics Seminar, Rice University, September 6, 2012*Injectivity of satellite operators on knot concordance.*Topology Seminar, Rice University, August 27, 2012*Slice knots which bound Klein bottles.*Topology Seminar, Rice University, August 20, 2012*The oriented cobordism ring, Thom spaces and transversality (§17-18).*Characteristic Classes seminar: based on Milnor & Stasheff's Characteristic Classes, Rice University, August 8-10, 2012*Wu's formula for Stiefel-Whitney classes (part of §11).*Characteristic Classes seminar: based on Milnor & Stasheff's Characteristic Classes, Rice University, July 13, 2012*The Thom isomorphism theorem (§10).*Characteristic Classes seminar: based on Milnor & Stasheff's Characteristic Classes, Rice University, July 2-6, 2012*Introducing Stiefel-Whitney classes (§1-4).*Characteristic Classes seminar: based on Milnor & Stasheff's Characteristic Classes, Rice University, June 11-14, 2012*Kinky disks and Casson handles.*VIGRE Topology Seminar, Rice University, April 3, 2012*Introducing the uncertainty principle in analysis.*Current Mathematics Seminar, Rice University, February 2, 2012*A topological interpretation of the Burau representation, and the Lawrence Krammer representation of the Braid group.*Braids Seminar, Rice University, November 14, 2011*On the signature of even 4-manifolds.*VIGRE Topology Seminar, Rice University, September 20, 2011*Braids in unexpected places.*Braids Seminar, Rice University, September 12, 2011*Introducing the Arf invariant.*Student Knot Invariants Seminar, July 11, 2011*An introduction to the philosophy of mathematics.*Student Mathematical Philosophy Seminar, Rice University, May 27, 2011*A duality theorem for infinite cyclic coverings.*VIGRE Topology Seminar, Rice University, April 19, 2011*Infinitely many hats, the axiom of choice, and predicting the future.*Current Mathematics Seminar, Rice University, April 7, 2011*The space of simple closed curves on a surface.*VIGRE Mapping Class Groups Seminar, Rice University, February 9, 2011*An elliptic curve, tessellations, and M.C. Escher.*Student Geometry Seminar, Rice University, June 1, 2010*An introduction to topological entropy of a dynamical system.*Current Mathematics Seminar, Rice University, February 25, 2010*Exploring the world of wavelets.*Best of GREAT Day presentations, SUNY Geneseo, April 24, 2009*Exploring the world of wavelets.*GREAT Day (Geneseo Recognizing Excellence, Achievement and Talent) Day, SUNY Geneseo, April 21, 2009*Developing Algorithms for the Determination of Relative Peptide Abundances from LC/MS Data.*Nebraska Conference for Undergraduate Women in Mathematics, University of Nebraska - Lincoln, February 1, 2009*Analysis of Inversions in Spherical and Hyperbolic Geometries.*GREAT Day (Geneseo Recognizing Excellence, Achievement and Talent) Day, SUNY Geneseo, April 22, 2008*Statistics of random DNA.*Frontiers of Computational Mathematics conference, New Jersey Institute of Technology, May 14, 2007

## Past and upcoming conferences

- Conference on 4-manifolds and knot concordance, Max Planck Institute for Mathematics, October 2016
- William Rowan Hamilton Geometry and Topology Workshop, Trinity College Dublin, Ireland, August 2016
- Topology in dimension 3.5: a conference in memory of Tim Cochran, Rice University, June 2016
- Rubermania: Workshop on Flavours of Gauge Theory, The Fields Institute, Toronto, ON, May 2016
- Joint Mathematics Meetings, Seattle, WA, January 2016
- CMS Winter Meeting, Montreal, QC, December 2015
- AMS Central Sectional Meeting, Loyola University, October 2015
- Princeton Low-Dimensional Topology Conference, Princeton University, June 2015
- Moab Topology Conference, Utah State University Regional Campus in Moab, May 2015
- AWM Research Symposium, University of Maryland, College Park, April 2015
- AMS Central Sectional Meeting, University of Wisconsin-Eau Claire, September 2014
- Workshop on Topology and Invariants of 4-manifolds, Simons Center for Geometry and Physics, August 2014
- Graduate Workshop on 4-manifolds, Simons Center for Geometry and Physics, August 2014
- Combinatorial Link Homology Theories, Braids, and Contact Geometry, Institute for Computational and Experimental Research in Mathematics (ICERM), August 2014
- Joint Mathematics Meetings, Baltimore, MD, January 2014
- Tech Topology Conference, Georgia Institute of Technology, December 2013
- AMS Central Sectional Meeting, Washington University at St. Louis, October 2013
- Rolfsenfest: Low-dimensional topology, knots, and orderable groups, International Center of Mathematical Meetings, July 2013
- Lehigh University Geometry and Topology Conference, Lehigh University, May 2013
- Hempelfest: 3-manifolds: Heegaard splittings, the curve complex, and hyperbolic geometry, Rice University, April 2013
- Texas Geometry and Topology Conference, Rice University, November 2012
- Midwest Topology Seminar, Michigan State University, October 2012
- AMS Central Sectional Meeting, University of Akron, October 2012
- Texas Algebraic Geometry Seminar, Rice University, April 2011
- The Fifth Triennial Ahlfors--Bers Colloquium, Rice University, March 2011
- Frontiers in Applied and Computational Mathematics, New Jersey Institute of Technology, May 2007
- Joint Mathematics Meetings, New Orleans, January 2007
- Nebraska Conference for Undergraduate Women in Mathematics, University of Nebraska - Lincoln, February 2009
- Nebraska Conference for Undergraduate Women in Mathematics, University of Nebraska - Lincoln, February 2008
- Hudson River Undergraduate Mathematics Conference, Skidmore College, April 2006

## Undergraduate research

*Honors Thesis in Mathematics (2008 - 2009)*

Document
Presentation
- Advisor: Dr. Olympia Nicodemi.
- State University of New York at Geneseo.
- Title: Exploring the connections between Fourier analysis and wavelets.
- Independent research, enrollment by invitation of Mathematics department.
- Presentation at the GREAT (Geneseo Recognizing Excellence, Achievement and Talent) Day, and Best of GREAT Day (Spring 2009).

*Research in Industrial Projects for Students (2009)*

Document
Presentation
Nebraska Presentation
- Joint work with Jake Marcus, Melanie Kanter and Anne Eaton.
- Mentors: Dr. Matteo Pellegrini, Dr. Shawn Cokus, and Dr. Parag Mallick.
- Institute of Pure and Applied Mathematics, University of California at Los Angeles.
- Worked with the Spielberg Family Center for Applied Proteomics on analyzing proteomic information based on Liquid Chromatography-Mass Spectrometry data.
- Presentation at the Nebraska Conference for Undergraduate Women in Mathematics (Spring 2009).

*Directed Study in Inversive Geometry (2007-08)*

Document
Presentation
- Mentor: Dr. Jeff Johannes.
- State University of New York at Geneseo.
- Determination and analysis of analogs of inversions in non-Euclidean geometries.
- Presentation at the GREAT (Geneseo Recognizing Excellence, Achievement and Talent) Day (Spring 2008).

*Research in Biomathematics (2006-07)*

Poster
- Joint work with Lauren Wood.
- Mentors: Dr. Wendy Pogozelski and Dr. Anthony Macula.
- State University of New York at Geneseo.
- Proof of principle of the theory of Group Testing to Annihilate Pairs.
- Poster presentation at the Joint Mathematical Meetings. (Spring 2007)
- Poster presentation at the GREAT (Geneseo Recognizing Excellence, Achievement and Talent) Day (Spring 2007)

*Research in Biomathematics (2007)*

Presentation
- Joint work with Aaron Young.
- Mentor: Dr. Anthony Macula.
- State University of New York at Geneseo.
- Developed a program to determine the expectation and variance of the free energy, enthalpy and entropy of a strand of DNA given certain information about the constituent base pairs.
- Presentation at the Frontiers of Computational Mathematics conference at New Jersey Institute of Technology (Spring 2007).

*Summer Undergraduate Research Fellowship Program (2007)*

Document
Presentation
- Advisor: Dr. Stephan Wilkens.
- State University of New York Upstate Medical University.
- Purification and characterization of certain domains of P-glycoprotein, a protein implicated in multidrug resistance, especially against cancer chemotherapy.
- Presentation at the GREAT (Geneseo Recognizing Excellence, Achievement and Talent) Day (Spring 2008).
- Presentation at BIOL 381: Introduction to Research, at SUNY Geneseo (Fall 2007)

*Student Research Workshop on Wavelets and Digital Image Compression (Fall 2007) *

- State University of New York at Geneseo.
- Participants selected based on academic record and faculty recommendation.