Jason Callahan - Research

Jason Callahan

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Mathematical Writing

Jørgensen Number and Arithmeticity. Conformal Geometry and Dynamics, Volume 13 (2009), 160-186.

The Arithmetic and Geometry of Two-Generator Kleinian Groups. PhD Thesis, The University of Texas at Austin. May 2009.

Conjugate Generators of Knot and Link Groups. Accepted for publication in Journal of Knot Theory and Its Ramifications, April 2009. Preprint available at arXiv:0806.3452v2.

Denominators of Boundary Slopes for (1,1)-Knots. Unpublished note.

Permutation Lattices of Finite Groups. Senior Honors Thesis, The University of Texas at Austin. May 2002.

Integrodifferential Equations. Research Experiences for Undergraduates Report, Penn State University. Summer 2000.

Grants and Honors

American Mathematical Society Graduate Student Travel Grant to the Joint Mathematics Meetings in Washington, DC, January 5 - 8, 2009, with matching funds from the Research Training Group in the Department of Mathematics at The University of Texas at Austin.

Graduate Research Assistantship. The University of Texas at Austin. Spring 2009 and Summers 2004, 2006, and 2008.

VIGRE (Vertical InteGration of Research and Education) Graduate Traineeship. The University of Texas at Austin. Fall 2002 through Spring 2006.

International Centre for Mathematical Sciences Travel and Accommodations Support for Workshop on 3-manifolds after Perelman. Heriot-Watt University, Edinburgh. March 13-17, 2006.

National Science Foundation Graduate Research Fellowship, Honorable Mention. 2002.

Undergraduate VIGRE Grant (to fund research for senior honors thesis). The University of Texas at Austin. Fall 2001.

Research Experiences for Undergraduates (VIGRE grant funded stipend, living and travel expenses). Penn State University. Summer 2000.

Talks

The Arithmetic and Geometry of Two-Generator Kleinian Groups (my PhD defense). Topology Seminar, The University of Texas at Austin. April 17, 2009.

Jørgensen Groups. Junior Topology Seminar, The University of Texas at Austin. April 15, 2009.

Conjugate Generators of Knot and Link Groups. Topology Seminar, The University of Texas at Austin. April 21, 2008.

Jørgensen Groups. Junior Topology Seminar, The University of Texas at Austin. April 2, 2008.

Dirichlet's Unit Theorem. Junior Number Theory Seminar, The University of Texas at Austin. October 9, 2007.

Thurston's Hyperbolic Dehn Surgery Theorem. Junior Topology Seminar, The University of Texas at Austin. September 26, 2007.

Representations of Two-Bridge Knot and Link Groups. Junior Topology Seminar, The University of Texas at Austin. February 21, 2007.

Boundary Slopes for 2-Bridge Links. Junior Topology Seminar, The University of Texas at Austin. November 30, 2005.

The Finite Filling Conjecture (my PhD qualifying exam). Topology Seminar, The University of Texas at Austin. April 29, 2005.

A Proof of the Finite Filling Conjecture. Junior Topology Seminar, The University of Texas at Austin. April 20, 2005.

Introducing Khovanov Homology. Junior Topology Seminar, The University of Texas at Austin. November 24, 2004.

Introduction to and Computation of Witt Rings. Junior Algebra Seminar, The University of Texas at Austin. February 9, 2004.

Bilinear Forms. Sophex Seminar, The University of Texas at Austin. November 21, 2003.

Integrodifferential Equations. Mathematics Advanced Study Semester Fest Conference, Penn State University. July 29-31, 2000.

Conferences Attended and Seminars Organized

Joint Mathematics Meetings. Washington, DC. January 5-8, 2009.

40th Texas Geometry and Topology Conference. The University of Texas at Austin. October 10-12, 2008.

Junior Topology Seminar, Organizer. The University of Texas at Austin. 2006-2007.

Workshop on 3-manifolds after Perelman. Heriot-Watt University, Edinburgh. March 13-17, 2006.

34th Texas Geometry and Topology Conference. The University of Texas at Austin. Sept. 30-Oct. 2, 2005.

3-Manifolds and Knot Theory Conference (In Honor of Cameron Gordon's 60th Birthday). The University of Texas at Austin. May 23-25, 2005.

32nd Texas Geometry and Topology Conference. Texas A&M University. October 29-31, 2004.

Topology of Manifolds of Dimension 3 and 4 (In Honor of Andrew Casson's 60th Birthday). The University of Texas at Austin. May 19-21, 2003.

The Millennium Lectures. The University of Texas at Austin. Spring 2001.

Mathematics Advanced Study Semester Fest Conference, Penn State University. July 29-31, 2000.