Mathematics | natalie

Mathematics Research

My mathematics research has focused on algebraic geometry, representation theory, and combinatorics. Much of my work uses combinatorial techniques to explore properities of vector bundles of conformal blocks on the moduli space of curves. I am excited about the interactions between different areas of mathematics and collaborating with others in developing connections.

Preprints

Quantum Kostka and the rank one problem for sl_2m
- arXiv: 1508.06952 l 2016
- Macaulay2 programs to run algorithms with tableaux from paper.

Conformal blocks in type C at level one
- arXiv:1605.06184

Expository Mathematics

An introduction to algebraic geomety for Algebra Undergraduates

On GIT stability of pointed curves

Notes on trivialization of vector bundle on a curve with a fixed determinant

Notes on affine Lie algebras for the construction of conformal blocks

Representations of the symmetric group

Voting Theory, Senior Thesis

Mathematics Research Talks and Presentations

"Fundamental Group of SO(3)"

Fall 2013

“Quantum Kostka and the rank one problem for sl_2m”
- University of Illinois Urbana-Champaign, Algebra, Geometry, and Combinatoics, Champaign, IL, November, 2016.
- University of British Columbia, Discrete Mathematics Seminar, Vancouver, BC, November, 2016
“Identities and finite generate of divisors of conformal blocks”
- Ohio State University, Algebraic Geometry Seminar, Columbus, OH, November, 2016.
- University of Illinois Chicago, Algebraic Geometry Seminar, Chicago, IL, September 2016.
- University of Pennsylvania, Algebra Seminar, Pittsburgh, PA, September 2016
“Identities between first Chern classes of vector bundles of conformal blocks”
- University of Utah Algebraic Geometry Seminar, Salt Lake City, Utah, September 2016.
“Conformal blocks of type C at level one”
- AMS Central Sectional Meeting, North Dakota State University, April 2016.
"Moduli Space of Curves and Vector Bundles of Conformal Blocks"
- UGA Graduate Student Seminar, April 2016.
“Quantum Kostka and the rank one problem for sl_2m”
- AMS-MAA Joint Mathematics Meetings, Seattle, WA, January 2016.
- University of Washington Combinatorics Seminar, Seattle, WA, October 2015.
“A brief introduction to Schubert calculus”
- UGA Mock AMS Conference, July 2015.
“A construction on the moduli space of genus zero curves with n marked points”
- UGA Tuesday Algebraic Geometry Student Seminar, January 2015.
“Moduli stack of genus g, smooth, projective, connected curves”
- UGA String Theory VIGRE Research Group, April 2014.
“Moduli of complete conics”
- UGA Graduate Student Seminar, February 2014.
“The fundamental group of SO(3)”
- UGA Mock AMS Conference, July 2013.

Mathematics Conferences

Georgia Summer Workshop in Algebraic Geometry, UGA, Athens, GA. August 2016.
Chip Firing and Tropical Curves. MSRI Graduate Student School. July 2016.
MAAGC (Mid-Atlantic Algebraic Geometry and Combinatorics) Workshop, Drexel University, Philadelphia, PA, May 2016.
AMS Central Sectional Meeting, University of North Dakota, Fargo, NC, April 2016.
AMS-MAA Joint Mathematics Meetings, Seattle, WA, January 2016.
Georgia Algebraic Geometry Symposium (GAGS), Emory University, Atlanta, GA, October 2015.
Western Algebraic Geometry Symposium (WAGS), University of Washington, Seattle, WA, October 2015. Poster Presentation: “Quantum Kostka and the rank one problem for sl_2m.”
Algebraic Geometry Northeastern Symposium (AGNeS), Brown University, Providence, RI, October 2015. Poster Presentation: “Quantum Kostka and the rank one problem for sl_2m.”
Algebraic Geometry Graduate Student Boot Camp, University of Utah, Salt Lake City, UT, July 2015.
Women and Mathematics Program, Institute for Advanced Study (IAS), Princeton, NJ, May 2015.
AMS-MAA Joint Mathematics Meetings, San Antonio, TX, January 2015.
AMS Southeastern Sectional Meeting, University of North Carolina, Greensboro, NC, November 2014.
Georgia Algebraic Geometry Symposium (GAGS), University of Georgia, Athens, GA, October 2014.
Moduli and Automorphic Forms, Humbolt University, Berlin, Germany, May 2014.
Algebraic Geometry Northeastern Symposium (AGNeS), Stony Brook, NY, April 2014.
Georgia Algebraic Geometry Symposium (GAGS), University of Georgia, Athens, GA, October 2013.
AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2013.