# Graduate

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

Research Statement

Statement of Teaching Philosophy

## Publications

### Satellite operators with distinct iterates in knot concordance. Submitted.

### Casson towers and filtrations of the knot concordance group. Submitted.

### Satellite operators as group actions on knot concordance. Submitted. (With Christopher W. Davis.)

### Injectivity of satellite operators in knot concordance.

*Journal of Topology*, Advance Access published April 1, 2014, doi:10.1112/jtopol/jtu003, (With Tim D. Cochran and Christopher W. Davis).### Slice knots which bound punctured Klein bottles.

*Algebraic & Geometric Topology*, 13(5):2713-2731, 2013.

## Miscellaneous

### 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 advanced exam.

### Errors discovered in Knots and Links by Dale Rolfsen.

### Seminars organized

### Heegaard-Floer computationar, Spring 2014.

### Characteristic classes seminar, following Milnor & Stasheff's Characteristic Classes, Summer 2012.

### Knot invariants seminar, Summer 2011.

## 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*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*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

Document Presentation*Honors Thesis in Mathematics (2008 - 2009)*- 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).

Document Presentation Nebraska Presentation*Research in Industrial Projects for Students (2009)*- 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).

Document Presentation*Directed Study in Inversive Geometry (2007-08)*- 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).

Poster*Research in Biomathematics (2006-07)*- 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)

Presentation*Research in Biomathematics (2007)*- 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).

Document Presentation*Summer Undergraduate Research Fellowship Program (2007)*- 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.