Graduate


I graduated from the Rice Mathematics Department with a PhD in May 2014.

Research Statement
Statement of Teaching Philosophy


Publications


Miscellaneous


Past and upcoming talks


  • Casson towers and filtrations of the smooth knot concordance group. PhD Defense, Rice University, April 8, 2014
  • Satellite operators on knots, and fractals. STEM colloquium, University of Wisconsin-Eau Claire, March 7, 2014
  • 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
  • Satellite operators as group actions on knot concordance. AMS Central Sectional Meeting, Washington University at St. Louis, October 20, 2013
  • Casson towers and filtrations of the smooth knot concordance group. AMS Central Sectional Meeting, Washington University at St. Louis, October 19, 2013
  • 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
  • A friendly introduction to knots in three and four dimensions. Mathematics Department Colloquium, SUNY Geneseo, April 25, 2013
  • A brisk introduction to egendrian/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
  • 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
  • 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
  • On the signature of even 4-manifolds. VIGRE Topology Seminar, Rice University, September 20, 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
  • Characteristic Classes seminar, Rice University, Summer 2012: based on Milnor & Stasheff's Characteristic Classes.
    • The oriented cobordism ring, Thom spaces and transversality (§17-18). August 8-10, 2012
    • Wu's formula for Stiefel-Whitney classes (part of §11). July 13, 2012
    • The Thom isomorphism theorem (§10). July 2-6, 2012
    • Introducing Stiefel-Whitney classes (§1-4). June 11-14, 2012
  • Braids Seminar, Rice University, Fall 2011.
    • A topological interpretation of the Burau representation, and the Lawrence Krammer representation of the Braid group. November 14, 2011
    • Braids in unexpected places. September 12, 2011
  • 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


  • AMS Central Sectional Meeting, University of Wisconsin-Eau Claire, September 2014
  • Joint Mathematics Meetings, Baltimore, MD, January 2014
  • 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

Undergraduate


  • 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.
    • 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.