Anand Patel

Contact Info

Email: anand.patel@okstate.edu

Personal Website: https://sites.google.com/view/anand-patel

Employment

1. Associate Professor, Oklahoma State University, 2023 - present

2. Assistant Professor, Oklahoma State University, 2017 - 2023

3. Lecturer, Harvard University, 2016 - 2017

4. Visiting Assistant Professor (Post-doc), Boston College, 2013 - 2016

5. Graduate Teaching Fellow, Harvard University, 2009 - 2013

Education

1. Ph. D. in Mathematics, Harvard University, 2008 - 2013 (adviser: Joe Harris)

2. B.A. in Mathematics, University of California, Berkeley, Highest Honors, 2005 - 2008

Published Work

(Listed reverse-chronologically, by publication date. Only published papers included - for preprints, check out my website at https://sites.google.com/view/anand-patel/home.)

• Patel, Anand, Eric Riedl, and Dennis Tseng. "Moduli of linear slices of high degree hypersurfaces." Accepted for publication in Algebra & Number Theory. (2023)

• Lee, Mitchell, Anand Patel, and Dennis Tseng. "Equivariant degenerations of plane curve orbits." Transactions of the American Mathematical Society 376, no. 10 (2023): 6799-6843. 

• Deopurkar, Anand, and Anand Patel. "Vector bundles and finite covers." In Forum of Mathematics, Sigma, vol. 10, p. e40. Cambridge University Press, 2022.

• Patel, Anand, Ashvin Swaminathan. "Inflectionary invariants of isolated complete intersection curve singularities." Vol. 282, no. 1397. Memoirs of the American Mathematical Society, 2023.

• Patel, Anand, Ananth N. Shankar, and Junho Peter Whang. "The rank two p-curvature conjecture on generic curves." Advances in Mathematics 386 (2021): 107800.

• Bujokas, Gabriel, and Anand Patel. "Invariants of a General Branched Cover of P1." International Mathematics Research Notices (2021), no. 6 (2021): 4564-4604.

• Lee, Mitchell, Anand Patel, Hunter Spink, and Dennis Tseng. "Orbits in (Pr) n and equivariant quantum cohomology." Advances in Mathematics 362 (2020): 106951.

• Deopurkar, Anand, Eduard Duryev, Anand Patel. "Ramification Divisors of General Projections." Documenta Mathematica 25 (2020): 1917-1952

• Patel, Anand. "Independence of boundary divisors in the space of admissible covers." Proceedings of the American Mathematical Society 148, no. 4 (2020): 1383-1388.

• Landesman, Aaron, and Anand Patel. "Interpolation problems: Del Pezzo surfaces." Annali Scuola Normale Superiore-Classe di Scienze (2019): 1389-1428.

• Deopurkar, Anand, and Anand Patel. "Syzygy divisors on Hurwitz spaces." Contemporary Mathematics 703 (2018): 209-222.

• Chen, Dawei, and Anand Patel. "Extremal effective divisors of Brill–Noether and Gieseker–Petri type in." Advances in Geometry 16, no. 2 (2016): 231-242.

• Deopurkar, Anand, and Anand Patel. "The Picard rank conjecture for the Hurwitz spaces of degree up to five." Algebra & Number Theory 9, no. 2 (2015): 459-492.

• Deopurkar, Anand, and Anand Patel. "Sharp slope bounds for sweeping families of trigonal curves." Mathematical Research Letters 20, no. 5 (2013): 869-884.

Preprints

• Orbits of linear series on the projective line, with A. Deopurkar, 2022. (submitted)

• Lines highly tangent to a hypersurface, with E. Riedl, G. Smith, and D. Tseng, 2022. (submitted)

• A universal formula for counting cubic surfaces, with A. Deopurkar and D. Tseng, 2021. (submitted)

• Special codimension one loci in Hurwitz spaces, 2015.

Advising

• Supervised Aaron Landesman's Harvard undergraduate senior thesis, 2015 - 2016. (Aaron was runner up for the Morgan Prize.)

• Supervised Ashvin Swaminathan's Harvard undergraduate senior thesis 2016 - 2017. (Ashvin received the Morgan Prize.)

• Supervised Chapman Howard's' OSU undergraduate senior thesis on Impossibility theorems in Galois Theory (2018).

• Supervising Ray Shang's Harvard undergraduate senior thesis, 2023 - 2024.

• Ph. D. student(s): Steve Thakur, (2018). Thesis: Galois representations and reductions of abelian varieties over number fields

• Adam Cartisano, Thesis: Bounding Pinch Point Schemes of Projected Surfaces (2023)

Talks

• Graduate Algebraic Geometry Seminar, On the Picard Rank of the Trigonal and Tetragonal Loci, 2010

• Harvard - MIT Baby Algebraic Geometry Seminar, A few GIT examples, 2010

• Harvard GIT Seminar, Classical Invariant Theory: Examples, 2011

• Michigan Algebraic Geometry Seminar, 2012

• UIC Algebraic Geometry Seminar, 2012

• Rice University Algebraic Geometry Seminar, 2012

• Boston College Algebraic Geometry Seminar, 2012

• Brown Algebraic Geometry Seminar, 2012

• Harvard-MIT Algebraic Geometry Seminar, 2014

• Northeastern Algebraic Geometry Seminar, 2014

• Current Developments in Moduli Theory (Northeastern), 2014

• U. Michigan Algebraic Geometry Seminar, 2014

• Stanford Algebraic Geometry Seminar, 2015

• Brandeis Every Topic Seminar, 2015

• U. Wisconsin, Madison Moduli crossroads retreat (MXRI) graduate workshop lecture series, 2015

• Brown University AGNES graduate mini-school: The Maximal Rank Conjecture.

• Joint Mathematics Meetings, Jan. 8, 2015: Slopes of families of curves.

• Colloquium: Oklahoma State University. Feb. 8, 2016 Interpolation.

• Northeastern Geometry, Physics, and Representation Theory Seminar March 24, 2016.

• Tufts University Branched covers and the Steinitz problem March, 2018.

• Oklahoma State University Commutative Algebra Seminar Projection and Ramification May, 2018.

• Oklahoma State University High School Math Day Why being a geometry teacher is hard October, 2018

• Oklahoma State University Number Theory Seminar The p-curvature conjecture, two lectures in Spring 2019

• Notre Dame Algebraic Geometry seminar Projection and Ramification October 2019

• Colorado State University Algebraic Geometry seminar Projection and Ramification November 2019

• Stanford University Algebraic Geometry Seminar, Projection and Ramification February 2020

• Arizona State University AG Seminar, How Some Constructions in Projective Geometry Vary Oct 2020

• Seminario Nacional Geometria Algebraica, Enumerating Equations Equivariantly Nov 2021

• UIC Algebraic Geometry seminar, Counting hypersurfaces March 2022

• KU Geometry seminar, The number of times a hypersurface occurs April 2022

• Jornadas del seminario nacional de geometría algebraica, CIMAT - Guanajuato October 2022 Lecture series. Website and poster: https://www.matem.unam.mx/~lozano/jornadasSNGA2022.html

• Notre Dame Algebraic Geometry seminar, Counting cubic surfaces September 2023

Teaching

• Harvard University, Introductory Calculus (Math Ma), 2009

• Harvard University, Undergraduate Linear Algebra (21b), 2010

• Harvard University, Introductory Calculus (Ma), 2011

• Math Circle (Teaching gifted middle school students), 2011 - 2015.

• Boston College, Introductory Calculus, 2013.

• Boston College, Introduction to Abstract Algebra, 2014.

• Boston College, Introduction to Probability, 2014.

• Boston College, Advanced Calculus II, 2014.

• Boston College, Branched Covers, Spring 2015.

• Boston College, Calculus I, Fall 2016.

• Boston College, Linear Algebra, Spring 2016.

• Harvard University, Honors Linear Algebra and Multivariable Calculus, 2016-2017

• Harvard University, Topics course in Algebraic Geometry, Fall 2016

• Harvard University, Calculus 2, Spring 2017

• Oklahoma State University, Multivariable Calculus, Fall 2017

• Oklahoma State University, Introduction to Abstract Algebra, Spring 2018

• Oklahoma State University, Basic Algebraic Geometry, Fall 2018

• Oklahoma State University, Number Theory, Fall 2018

• Oklahoma State University, Algebraic Geometry II, Spring 2019

• Oklahoma State University, Linear Algebraic Groups I, Fall 2019

• Oklahoma State University, Geometry, Fall 2019

• Oklahoma State University, Linear Algebraic Groups II, Spring 2020

• Oklahoma State University, Calculus II, Spring 2020

• Oklahoma State University, Calculus III, Summer 2020

• Oklahoma State University, Calculus II, Fall 2020

• Oklahoma State University, Abstract Algebra I, Fall 2020

• Oklahoma State University, Calculus II, Fall 2020

• Oklahoma State University, Abstract Algebra II, Spring 2020

• Oklahoma State University, Graduate Commutative Algebra, Spring 2020

• Oklahoma State University, Calculus III, Summer 2020

• Oklahoma State University, Intersection Theory Seminar, Spring 2021

• Oklahoma State University, Calculus III, Fall 2021

• Oklahoma State University, History of Mathematics, Fall 2021

• Oklahoma State University, Geometry, Fall 2022

• Oklahoma State University, Classical Algebraic Geometry, Fall 2022