Isabelle Shankar

I am a fifth year math graduate student at UC Berkeley and am advised by Serkan Hoşten. I expect to graduate in May 2021. Immediately after I will be joining the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany for the remainder of 2021 and then start my position as a J.L. Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign in January 2022.

My research interests include convex algebraic geometry, optimization, and combinatorics, with particular interest in problems that have symmetries to exploit.

I am grateful for the support of the James H. Simons Fellowship and the UC Dissertation-Year Fellowship.

Contact

Email: "my first name"_"my last name" at berkeley dot edu
Office: 739 Evans

Research

The degree of the central curve in semidefinite programs with Serkan Hoşten and Angélica Torres (preprint)
- Invited to contribute to the LSSM collaboration project at MPI Leipzig (https://www.orlandomarigliano.com/lssm)
Symmetry Adapted Gram Spectrahedra with Alexander Heaton and Serkan Hoşten (preprint)

Sums of Squares and Symmetric Ternary Quartics

An SOS counterexample to an inequality of symmetric functions with Alexander Heaton
- To appear in the Journal of Pure and Applied Algebra

Presentations and Posters

Symmetry-Adapted Gram Spectrahedra (slides)

JMM Special Session on Optimization and Algebraic Geometry, Washington DC, January 2021
Combinatorics Seminar, University of Washington, December 2020
Discrete Math Seminar, University of Massachusetts Amherst, October 2020
Algebraic Statistics 2020 virtual mini-conference, University of Hawaii at Manoa, June 2020
Algebra and Discrete Math Seminar, UC Davis, February 2020
Nonlinear Algebra Seminar, UC Berkeley, January 2020

An SOS counterexample to an inequality of symmetric functions

The UC Berkeley combinatorics seminar, April 2020 (Zoom link , Password: T2%**7s6)

Symmetry Polynomials and Sums of Squares

Algebra, Geometry, and Combinatorics Seminar, San Francisco State University, October 2019
Max Planck Institute for Mathematics in the Sciences, May 2019

Sums of Squares Decomposition of Symmetric Polynomial Inequalities (poster)

Workshop on Applied Algebra, TU Braunschweig, Germany, June 2019

Conferences and Travel

Upcoming:

Queer and Trans Mathematicians in Combinatorics, Fields Institute, Toronto, Canada, June 2021

JMM Special Session on Optimization and Algebraic Geometry, Washington DC, January 2021
Symmetry, Randomness, and Computations in Real Algebraic Geometry, ICERM, August 2020
AMS Spring Western Sectional Meeting, Fresno, CA (invited to speak, but event canceled), May 2020
AMS Spring Western Sectional Meeting, Purdue University (invited to speak, but event canceled), April 2020
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, Summer 2019
SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland, July 2019
Workshop in Applied Algebra, TU Braunschweig, Germany, June 2019
Optimization, Algebra, Geometry & Statistics: Serkan Hosten's Mathematics @ 50, San Francisco State University, February 1, 2019
Real Algebraic Geometry and Optimization workshop, Nonlinear Algebra Program, ICERM, Fall 2018
Summer School on Hyperbolic Polynomials, Sums of Squares, and Optimization, Georgia Tech, Summer 2018
6th Encuentro Colombiano de Combinatoria (ECCO), Universidad del Norte, Barranquilla, Colombia, Summer 2018

Teaching

In 2018, I was awarded the Outstanding Graduate Student Instructor Award.

Fall 2019: GSI for Math 54 - Linear Algebra & Differential Equations with Prof. Constantin Teleman.

Fall 2018: GSI for Math 1B - Calculus II with Prof. Emiliano Gomez.

Spring 2018: GSI for Math 1B - Calculus II with Prof. Mark Haiman.

Fall 2017: GSI for Math 1A - Calculus I with Prof. Vivek Shende.

Spring 2017: GSI for Math 1A - Calculus I with Prof. Mark Haiman.

Fall 2016: GSI for Math 32 - Precalculus with Alexander Appleton.