I received my Ph.D. in mathematics from the University of North Carolina, Chapel Hill in 2018 under the supervision of Shrawan Kumar. After graduation I served as a visiting assistant professor in the department of mathematics at Bucknell University.

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My thesis research was in the area of algebraic geometry and geometric representation theory. More specifically, I studied the cohomology and K-theory of flag varieties. Together, my advisor and I demonstrated positivity of the Schubert structure constants in torus-equivariant K-theory of Kac-Moody flag varieties. You can find links to my thesis and papers below.  

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Research Papers:

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• Positivity in T-equivariant K-theory of flag varieties associated to Kac-Moody groups II (joint with Shrawan Kumar). Representation Theory 21, 35-60 (2017).

• An explicit determination of the K-theoretic structure constants of the affine Grassmannian associated to SL2.

• Positivity in T-equivariant K-theory of Kac-Moody flag varieties. (Ph.D. thesis)

 

Research Talks:

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• Southeastern Lie Theory X, University of Georgia (June 10, 2018)

• AMS Spring Southeastern Sectional Meeting, Special Session on Algebraic Geometry, Representation Theory, and Applications, Vanderbilt University (April 15, 2018)

• AMS and MAA Joint Mathematics Meeting, Contributed Session on Algebraic Geometry, San Diego, CA (January 11, 2018)

• Algebra Seminar, Rutgers University (December 6, 2017)

• Algebra Seminar, University of Virginia (October 18, 2017)

• Algebra Seminar, Virginia Tech (October 6, 2017)

• Algebraic Geometry Seminar, Ohio State University (October 3, 2017)

• Triangle Area Graduate Mathematics Conference, Duke University (April 23, 2017)

• Algebraic Geometry Seminar, Duke University (March 31, 2017)

• AMS Spring Southeastern Sectional Meeting, Special Session on Geometric Methods in Representation Theory, College of Charleston (March 12, 2017)

• Algebra and Combinatorics Seminar, North Carolina State University (January 30, 2017)

• Triangle Area Graduate Mathematics Conference, University of North Carolina, Chapel Hill (December 3, 2016)

• AMS Fall Southeastern Sectional Meeting, Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, North Carolina State University (November 13, 2016)

• Algebra & Discrete Mathematics Seminar, University of California, Davis (October 3, 2016)

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Teaching:

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Bucknell University:

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• Calculus I: Math 201, Section 21 (Fall 2018)

• Caluclus III: Math 211, Sections 5 and 6 (Fall 2018) 

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University of North Carolina, Chapel Hill:

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• Linear Algebra for Applications: Math 547, Section 1 (Summer 2017, Session 1) 

• Discrete Mathematics: Math 381, Section 2 (Spring 2017) 

• Discrete Mathematics: Math 381, Section 3 (Spring 2016)  

• Discrete Mathematics: Math 381, Section 5 (Fall 2015) 

• Calculus III: Math 233, Section 1 (Summer 2015, Session 2) 

• Calculus I: Math 231, Section 1 (Summer 2014, Session 1) 

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In August of 2016 I ran the week-long bootcamp on linear algebra for incoming graduate students at UNC.