Publications


Miscellaneous


Seminars/conferences/special sessions co/organized

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-(K) to CFD^(S3-K). Heegaard-Floer computationar, Rice University, April 2, 2014
  • 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

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.