# Anand Deopurkar

Mathematical Sciences Institute

The Australian National University

Canberra, ACT, 2601, Australia

`anand.deopurkar`

at `anu`

dot `edu`

dot `au`

(pgp)

4.56 Hanna Neumann Building

+61 2 6125 4628

## Table of Contents

I am an algebraic geometer with broad interests. Being an algebraic geometer means that I fundamentally study solution spaces of algebraic equations. I am interested in classical algebraic geometry, enumerative geometry, deformation theory, algebraic stacks, derived categories, among other things.

This semester (2022 Semester 2), I am teaching Algebra 1 and a course about mathematical communication called “The language of mathematics”.

## Papers/pre-prints

*Vector bundles and finite covers*.

Forum of Mathematics, Sigma (accepted), with Anand Patel (pdf, arXiv).

Talks: Adelaide (slides), Jeju Island (notes).*A universal formula for counting cubic surfaces*.

Pre-print, arxiv:2109.12672, with Anand Patel, Dennis Tseng (arxiv).

Talk: Cambridge (notes).*Spherical objects and stability conditions on CY2 quiver categories*.

Pre-print, arXiv:2108.09155, with Asilata Bapat, Anthony Licata (arxiv).*Stable log surfaces, admissible covers, and canonical curves of genus 4*.

Transactions of the Americal Mathematical Society 374, No. 1, 589-641 (2021), with Changho Han (pdf, arxiv).

Talk: Sydney (notes).*A Thurston compactification of the space of stability conditions*.

Pre-print, arXiv:2011.07908, with Asilata Bapat, Anthony Licata (arxiv).

Talks: Bonn (slides), Mumbai (slides), Amidale (slides), Sydney (notes).*Ramification divisors of general projections*.

Documenta Mathematica 25, 1917–1952 (2020), with Eduard Duryev, Anand Patel (pdf, arxiv).

Talks: Mexico (slides), San Diego (slides).*Anticanonical tropical cubic del Pezzos contain exactly 27 lines*.

Pre-print, arXiv:1906.08196, with María Angélica Cueto (arxiv).*Covers of stacky curves and limits of plane quintics*.

Transactions of the Americal Mathematical Society, 371, 549–588 (2019) (pdf, arxiv).

Talks: Boston (notes), Salt Lake City (poster).*Syzygy divisors on Hurwitz spaces*.

Contemporary Mathematics 703, 209–222 (2018), with Anand Patel (pdf, arxiv).*The canonical syzygy conjecture for ribbons*.

Mathematische Zeitschrift 288, No. 3-4, 1157–1164 (2018) (pdf, arxiv).

Talk: Melbourne (notes).*Toward GIT stability of syzygies of canonical curves*.

Algebraic Geometry 3, No. 1, 1–22 (2016), with Maksym Fedorchuk, David Swinarski (arxiv, journal).

Talks: Daejeon (slides), Pohang (notes).*The Picard rank conjecture for the Hurwitz spaces of degree up to five*.

Algebra & Number Theory 9, No. 2, 459–492 (2015), with Anand Patel (pdf, arxiv, journal).*Groebner techniques for ribbons*.

Albanian Journal of Mathematics 8, No. 2, 55–70 (2014), with Maksym Fedorchuk, David Swinarski (pdf, journal).*Compactifications of Hurwitz spaces*.

International Mathematics Research Notices 2014, No. 14, 3863–3911 (2014) (pdf, arxiv, journal).

Talks: Palo Alto (notes), Cambridge (notes).*Class of the Hodge eigenbundle using orbifold Riemann-Roch*.

Pre-print, appendix to*Cyclic covering morphisms on \(\overline M_{0,n}\)*by Maksym Fedorchuk (pdf).*Sharp slope bounds for sweeping families of trigonal curves*.

Mathematical Research Letters 20, No. 5, 869–884 (2013), with Anand Patel (pdf, arxiv, journal).

Talk: Boston (poster).*Modular compactifications of the space of marked trigonal curves*.

Advances in Mathematics 248, 96–154 (2013) (pdf, arxiv).

Talk: Cambridge (poster).*Alternate compactifications of Hurwitz spaces*.

Thesis, Harvard, 2012 (pdf).

Talks: Palo Alto (notes), Cambridge (notes).

## Teaching

Notes and other materials from some of my courses:

- Algebraic Geometry (Algebra 3), 2021.
- Foundations of Algebraic Geometry (Schemes), 2020.
- Algebraic Geometry (Algebra 3), 2019.
- Algebraic curves, 2017.
- Moduli of curves, 2014.

## Talks

Notes or slides for many of my talks are linked in the section on papers/pre-prints. Here are some additional talks:

*The geometry and combinatorics of Harder–Narasimhan filtrations*(slides)

Braids in representation theory and algebraic combinatorics, Institute for Computational and Experimental Research in Mathematics, Providence, Rhode Island.*The geometry of Fermat-like equations*(expository) (notes)

Trimester program on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishthana, Pune, India.*Algebraic curves and Belyi’s theorem*(expository) (notes)

Trimester program on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishthana, Pune, India.*Error correcting codes*(expository) (slides)

ANU Mathematics Extension Program, Canberra, Australia.*The work of Claire Voisin*(expository) (slides)

Women in mathematics day, Australian National University, Canberra, Australia.*Geometry of Hurwitz spaces*(notes)

Character varieties and topological quantum field theory, University of Auckland, Auckland, New Zealand.*The work of Caucher Birkar*(expository) (notes)

Colloquium, Australian National University, Canberra, Australia.*How to count using (co)homology*(expository) (notes)

Tata Institute of Fundamental Research, Mumbai, India.*Quadrature and algebraic geometry*(slides)

Workshop on algebraic geometry approximation, and optimization, MATRIX, Creswick, Victoria, Australia.

## Odds and ends

- GIT for syzygies of genus 7 curves

This is an ongoing project to determine GIT stability for syzygies of genus 7 canonical curves. This is the first genus where canonical syzygies define an interesting GIT quotient, so it would be nice to understand the complete picture. One day… - Categorical braid group actions

With Asilata Bapat, I wrote`Sage`

code to make explicit computations in the homotopy category of projective modules over a ring. In particular, this code can compute braid actions on complexes of projective modules over the zig-zag algebra of a quiver. - MSI course graph

This is an interactive dependency graph of ANU math department’s course catalogue. - A mystery hunt style puzzle
- Some visualisations
- Notes from some past seminars
- DbCoh: ANU, 2021
- Mixed hodge modules: UGA, 2017
- Stable rationality: Columbia, 2016