PhD progress

I am currently in year 4 of the PhD program here at Rice. I recently completed all requirements for PhD candidacy.

Publications

• Tim D. Cochran, Christopher W. Davis and Arunima Ray. Injectivity of satellite operators in knot concordance. Preprint

• Arunima Ray. Slice knots which bound Klein bottles. Preprint

Miscellaneous

• Syllabus for advanced exam.

• Errors discovered in Knots and Links by Dale Rolfsen.

• Organized a seminar on characteristic classes of vector bundles following Milnor & Stasheff's Characteristic Classes in Summer 2012.

• Organized a seminar on knot invariants in Summer 2011.

Past and upcoming talks

• AMS Sectional Meeting, University of Akron.

  • Slice knots which bound Klein bottles. October 20, 2012

• Topology Seminar, Rice University.

  • Injectivity of satellite operators on knot concordance. August 27, 2012
  • Slice knots which bound Klein bottles. August 20, 2012

• VIGRE Topology Seminar, Rice University.

  • Legendrian/transverse knots and their applications to (usual) knot theory and knot concordance. January 29, 2013
  • Symmetries of knots. September 21, 2012
  • Kinky disks and Casson handles. April 3, 2012
  • On the signature of even 4-manifolds. September 20, 2011
  • A duality theorem for infinite cyclic coverings. April 19, 2011

• Current Mathematics Seminar, Rice University.

  • Generating functions and random walks. September 6, 2012
  • Introducing the uncertainty principle in analysis. February 2, 2012
  • Infinitely many hats, the axiom of choice, and predicting the future. April 7, 2011
  • An introduction to topological entropy of a dynamical system. 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

• Knot invariants seminar, Rice University, Summer 2011.

  • Introducing the Arf invariant. July 11, 2011

• Student Mathematical Philosophy Seminar, Rice University, Summer 2011.

  • An introduction to the philosophy of mathematics. May 27, 2011

• VIGRE Mapping Class Groups Seminar, Rice University, Spring 2011.

  • The space of simple closed curves on a surface. February 9, 2011

• Student Geometry Seminar, Rice University, Summer 2010.

  • An elliptic curve, tessellations, and M.C. Escher. June 1, 2010

• 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.
  • 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.