Talks
Below is a roughly reverse chronological list of my papers and pre-prints, together with abstracts, links to notes or slides, and other commentary.
Be wise, equivariantise!
| when | 2026 |
| where | Sydney, Australia |
| venue | Workshop in algebraic geometry, University of Sydney |
| links | notes |
In a pencil of plane cubics, how many times do we see a given \(j\) invariant? Among the hyperplane slices of a cubic threefold, how many times does a given cubic surface appear? These counting problems, and many others, admit beautiful solutions using equivariant geometry. I will explain this method and the plethora of other questions that it opens up.
This talk was based on Equivariant classes of orbits in GL(2)-representations and A universal formula for counting cubic surfaces.
How to count using equivariant cohomology
| when | 2026 |
| where | Chennai, India |
| venue | Geometric and category-theoretic approaches to conformal field theory, Banff International Research Institute/Chennai Mathematical Institute |
In a pencil of cubic curves, how many times do we see a given j-invariant? Among the slices of a plane quintic curve, how many times do we see a given isomorphism class of 5-points on the line? These enumerative questions go under the name of “fixed moduli Gromov–Witten theory”. They involve counting objects of a given moduli (isomorphism class) satisfying certain conditions. While we have an array of tools to answer such questions for curves, we know embarrassingly little for surfaces and beyond. I will explain an approach to think about fixed moduli Gromov–Witten theory using equivariant geometry. As an application, I will give a universal solution to fixed moduli Gromov–Witten theory of generic cubic surfaces. This is based on joint work with Anand Patel, Dennis Tseng, and Oliver Li.
This talk was based on Equivariant classes of orbits in GL(2)-representations and A universal formula for counting cubic surfaces.
A Thurston compactification of the space of stability conditions
| when | 2025 |
| where | Creswick, Australia |
| venue | Teichmuller theory and flat structures, MATRIX |
| links | notes |
There is a close connection between metric geometry of a surface and homological algebra, which suggests that techniques from one domain should have counterparts in the other domain. Exploring this theme, we compactify the space of Bridgeland stability conditions using a construction similar to Thurston’s compactification of the Teichmuller space. I will describe this compactification and its boundary in a few examples with the hope to generate speculation about the general case. Based on joint work with Asilata Bapat and Tony Licata.
This talk was based on A Thurston compactification of the space of stability conditions.
The enumerative geometry of orbit closures
| when | 2025 |
| where | Melbourne, Australia |
| venue | Pure mathematics seminar, University of Melbourne |
Take a degree d form in n variables. What can we say about its GL(n) orbit? In particular, what is its degree? For n = 1 and 2, the answers were known by the year 1900. For n = 3, Carel Faber and Paolo Aluffi found the answers around the year 2000. I will discuss recent progress in higher dimensions on this and related questions, and the intricate geometry that seems to govern the answers. Based on joint work with Anand Patel and Dennis Tseng.
This talk was based on Equivariant classes of orbits in GL(2)-representations and A universal formula for counting cubic surfaces.
How twisty is that orbit?
| when | 2024 |
| where | Auckland, New Zealand |
| venue | Computations and applications of commutative algebra and algebraic geometry, NZMS-AustMS-AMS |
| links | slides |
Fix a polynomial \(P\). How complicated is the set of all polynomials obtained from \(P\) by changes of coordinates? This question, and many others, generalise as follows: given a representation an algebraic group, how complicated is the orbit of a given element? I will describe some answers, featuring toric varieties, Newton polyhedra, and stacks.
This talk was based on Equivariant classes of orbits in GL(2)-representations and A universal formula for counting cubic surfaces.
The work of Maryam Mirzakhani
| when | 2024 |
| where | Canberra, Australia |
| venue | Australian National University |
| comments | expository, |
| links | notes |
| labels | expository |
This was an expository talk explaining the work of Maryam Mirzakhani on the occasion of Women in Maths Day. I explained her work on the asymptotics of the number of geodesics on a hyperbolic surface to a general mathematical audience.
Papercraft
| when | 2024 |
| where | Canberra, Australia |
| venue | ANU Mathematics Extension Program |
| comments | expository |
| links | online board |
| labels | expository |
This talk was based on Paul Seidel’s Lectures on geometry and topology in the plane, Lecture 1 on cutting/regluing polygons. The talk was on zoom.
My origami directions call for a square, but I have an A4-sized rectangle. But I also have scissors! Can I cut the rectangle and reglue the pieces to get a square? More generally, when can I cut a shape A and reglue it to make another shape B? Come to the talk and find the answer. Scissors, tape, and paper optional, but recommended!
The geometry of stability conditions
| when | 2024 |
| where | Oberwolfach, Germany |
| venue | Artin groups meet triangulated categories, Mathematisches Forschungsinstitut Oberwolfach |
| links | extended abstract |
This was a talk based on A Thurston compactification of the space of stability conditions and Spherical objects and stability conditions on 2-Calabi–Yau quiver categories.
How to count using equivariant cohomology
| when | 2024 |
| where | Cambridge, UK |
| venue | Workshop on computational and applied algebraic geometry, Isaac Newton Institute |
This was a talk based on A universal formula for counting cubic surfaces.
How to count using equivariant cohomology
| when | 2024 |
| where | London, UK |
| venue | Imperial College |
This was a talk based on A universal formula for counting cubic surfaces.
Stability conditions, metrics, and compactifications
| when | 2024 |
| where | Edinburgh, UK |
| venue | School of Mathematics |
| links | notes |
This was a talk based on A Thurston compactification of the space of stability conditions.
Stability conditions, metrics, and compactifications (lecture series)
| when | 2023 |
| where | Haifa, Israel |
| venue | Summer school 2023 on algebraic geometry: derived categories, stability conditions, and moduli, Technion |
| links | notes |
This mini course consisted of 3 lectures of 1.5 hours each. This was based on A Thurston compactification of the space of stability conditions and ideas surrounding it.
Braids, automata, and the PL-sphere
| when | 2023 |
| where | Canberra, Australia |
| venue | Braids: algebra and geometry, Australian National University |
| links | notes |
This talk is based on the ideas A sphere of spherical objects. You see that it took us a couple of years to finish writing the paper!
Carpentry, geometry, and category theory
| when | 2022 |
| where | Chennai, India |
| venue | Chennai Mathematical Institute |
| links | notes |
This talk was based on an idea to contract stability manifolds for certain categories using techniques from rigidity theory. We have still not finished writing up all the details.
Error correcting codes
| when | 2022 |
| where | Canberra, Australia |
| venue | ANU Mathematics Extension Program |
| comments | expository |
| links | slides |
| labels | expository |
How to count using equivariant cohomology
| when | 2022 |
| where | Canberra, Australia |
| venue | Australian National University |
This was based on A universal formula for counting cubic surfaces.
Combinatorics and dynamics of Harder-Narasimhan filtrations
| when | 2022 |
| where | Beijing, China |
| venue | Tsinghua University (Online) |
| links | slides |
This was based on A sphere of spherical objects.
Braids and monodromy in algebraic geometry
| when | 2022 |
| where | Providence, Rhode Island |
| venue | Braids in Symplectic and Algebraic Geometry, ICERM, Brown University |
| comments | expository |
| labels | expository |
This was an expository pre-talk for the workshop Braids in symplectic and algebraic Geometry at ICERM.
How to count using equivariant cohomology
| when | 2022 |
| where | Cambridge, Massachusetts |
| venue | Harvard University |
| links | notes |
This was based on A universal formula for counting cubic surfaces.
Apparent boundaries of projective varieties
| when | 2022 |
| where | Providence, Rhode Island |
| venue | Brown University |
This was based on Ramification divisors of general projections.
The geometry and combinatorics of Harder–Narasimhan filtrations
| when | 2022 |
| where | Providence, Rhode Island |
| venue | Braids in representation theory and algebraic combinatorics, Institute for Computational and Experimental Research in Mathematics |
| links | notes |
This was based on the future paper A sphere of spherical objects.
The geometry of Fermat-like equations
| when | 2022 |
| where | Pune, India |
| venue | Trimester program on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishthana |
| comments | expository |
| links | notes |
| labels | expository |
This is the second talk I gave this trimester program. I explained the argument by Darmon and Granville that “hyperbolic” Fermat-like equations(\(A x^l + B y^m = C z^n\) where \(1/l + 1/m + 1/p < 1\)) have only finitely many integral solutions. The theorem and the proof is an orbifold version of Faltings’s theorem that hyperbolic curves have only finitely many rational points.
Also see the expository article I wrote accompanying the talks.
Algebraic curves and Belyi’s theorem
| when | 2021 |
| where | Pune, India |
| venue | Trimester program on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishthana |
| comments | expository |
| links | notes |
| labels | expository |
This is the first talk I gave in this trimester program. I explain the statement and proof of Belyi’s famous theorem.
Also see the expository article I wrote accompanying the talks.
Error correcting codes
| when | 2021 |
| where | Canberra, Australia |
| venue | ANU Mathematics Extension Program |
| comments | expository |
| links | slides |
| labels | expository |
A Thurston compactification of the space of stability conditions
| when | 2021 |
| where | Bonn, Germany |
| venue | Workshop on compactifications of stability manifolds (Online), Max Planck institute für Mathematics |
| links | notes |
This talk was based on A Thurston compactification of the space of stability conditions.
A Thurston compactification of the space of stability conditions
| when | 2021 |
| where | Mumbai, India |
| venue | Tata Institute of Fundamental Research (Online) |
| links | notes |
This talk was based on A Thurston compactification of the space of stability conditions.
A Thurston compactification of the space of stability conditions
| when | 2021 |
| where | Kraków, Poland |
| venue | Jagiellonian University (Online) |
This talk was based on A Thurston compactification of the space of stability conditions.
A Thurston compactification for categories
| when | 2020 |
| where | Amidale, Australia |
| venue | Topology session, AustMS (Online), University of New England |
| links | notes |
This talk was based on A Thurston compactification of the space of stability conditions.
Apparent boundaries of projective varieties
| when | 2020 |
| where | Oaxaca |
| venue | Seminario nacional de geometria algebraica (Online joint seminar of multiple universities in Mexico) |
| links | notes |
This talk was based on Ramification divisors of general projections.
Apparent boundaries of projective varieties
| when | 2020 |
| where | San Diego, California |
| venue | University of California (Online) |
| links | notes |
This talk was based on Ramification divisors of general projections.
Groups, spherical twists, and stability conditions
| when | 2019 |
| where | Sydney, Australia |
| venue | Workshop on triangulated categories in geometry and representation theory, University of Sydney |
| comments | part of a series with Asilata Bapat and Anthony Licata |
| links | notes |
This talk was based on A Thurston compactification of the space of stability conditions.
Log surfaces of almost K3 type and curves of genus 4
| when | 2019 |
| where | Sydney, Australia |
| venue | Birational geometry and moduli spaces, University of Sydney |
| links | notes |
This talk was based on Stable log surfaces, admissible covers, and canonical curves of genus 4.
The work of Claire Voisin
| when | 2019 |
| where | Canberra, Australia |
| venue | Women in mathematics day, Australian National University |
| comments | expository |
| links | notes |
| labels | expository |
Geometry of Hurwitz spaces
| when | 2018 |
| where | Auckland, New Zealand |
| venue | Character varieties and topological quantum field theory, University of Auckland |
| links | notes |
On the geometric Steinitz problem
| when | 2018 |
| where | Adelaide, Australia |
| venue | Number theory session, AustMS, University of South Australia |
| links | notes |
This talk was based on Vector bundles and finite covers.
The work of Caucher Birkar
| when | 2018 |
| where | Canberra, Australia |
| venue | Australian National University |
| comments | expository |
| links | notes |
| labels | expository |
This was an expository talk in the Fields Medal Colloquium in our department. We explained the work of a fields medallist to a general mathematical audience.
Moduli of almost K3 log surfaces and curves of genus 4
| when | 2018 |
| where | Xiamen, China |
| venue | Algebraic surfaces and related topics, Xiamen University |
This talk was based on Stable log surfaces, admissible covers, and canonical curves of genus 4.
How to count using (co)homology
| when | 2018 |
| where | Mumbai, India |
| venue | Tata Institute of Fundamental Research |
| comments | expository |
| links | notes |
| labels | expository |
This was an expository talk for undergraduate students. Through examples, I explained how to use the cup product in cohomology (more precisely, its dual, the intersection product on homology) to solve some counting problems. This was inspired by a similar talk by Rahul Pandharipande that I heard when I was an undergraduate.
What are ribbons and what do they tell us about Riemann surfaces
| when | 2018 |
| where | Bengaluru, India |
| venue | Indian Institute of Science |
This talk was based on The canonical syzygy conjecture for ribbons.
What are ribbons and what do they tell us about Riemann surfaces
| when | 2018 |
| where | Melbourne, Australia |
| venue | Monash University |
| links | notes |
This talk was based on The canonical syzygy conjecture for ribbons.
On the critical loci of finite maps
| when | 2018 |
| where | Canberra, Australia |
| venue | Australian National University |
This talk was based on Ramification divisors of general projections.
Quadrature and algebraic geometry
| when | 2018 |
| where | Creswick, Victoria, Australia |
| venue | Workshop on algebraic geometry approximation, and optimization, MATRIX |
| links | notes |
Vector bundles and finite covers
| when | 2017 |
| where | Chapel Hill, North Carolina |
| venue | Workshop on topics in algebraic geometry, University of North Carolina |
This talk was based on Vector bundles and finite covers.
Vector bundles and finite covers
| when | 2017 |
| where | Athens, Georgia |
| venue | University of Georgia |
This talk was based on Vector bundles and finite covers.
How to count using topology
| when | 2017 |
| where | Tacoma, WA |
| venue | Canada/USA Mathcamp |
| comments | expository |
| labels | expository |
Quivers and their representations
| when | 2017 |
| where | Pune, India |
| venue | Indian Institute of Science Education and Research |
Vector bundles and finite covers
| when | 2017 |
| where | Atlanta, Georgia |
| venue | Emory University |
This talk was based on Vector bundles and finite covers.
Geometry of moduli spaces
| when | 2016 |
| where | Canberra, Australia |
| venue | Australian National University |
Vector bundles and finite covers
| when | 2016 |
| where | Jeju Island, South Korea |
| venue | Conference on moduli and birational geometry |
| links | notes |
This talk was based on Vector bundles and finite covers.
Vector bundles and finite covers
| when | 2016 |
| where | Pune |
| venue | Indian Institute of Science Education and Research |
This talk was based on Vector bundles and finite covers.
Ribbons and Green’s conjecture
| when | 2016 |
| where | Columbia, South Carolina |
| venue | University of South Carolina |
This talk was based on The canonical syzygy conjecture for ribbons.
Ribbons and Green’s conjecture
| when | 2016 |
| where | Athens, Georgia |
| venue | University of Georgia |
This talk was based on The canonical syzygy conjecture for ribbons.
Cycles on Hurwitz spaces
| when | 2016 |
| where | Providence, Rhode Island |
| venue | Workshop on cycles on moduli spaces, geometric invariant theory, and dynamics, Institute for Computational and Experimental Research in Mathematics |
The algebra of canonical curves and the geometry of their moduli space
| when | 2016 |
| where | Athens, Georgia |
| venue | University of Georgia |
Picard groups of Hurwitz spaces
| when | 2016 |
| where | Seattle, Washington |
| venue | Higher genus curves and fibrations of higher genus curves in mathematical physics and arithmetic geometry II, AMS joint mathematics meetings |
This talk was based on The Picard rank conjecture for the Hurwitz spaces of degree up to five.
Limits of plane quintics via covers of stacky curves
| when | 2016 |
| where | Seattle, Washington |
| venue | Moduli spaces in algebraic geometry I, AMS joint mathematics meetings |
This talk was based on Covers of stacky curves and limits of plane quintics.
Limits of plane quintics via covers of stacky curves
| when | 2015 |
| where | Boston, Massachusetts |
| venue | Boston College–Northeastern algebraic geometry conference, Northeastern University |
| links | notes |
This talk was based on Covers of stacky curves and limits of plane quintics.
Limits of plane quintics via covers of stacky curves
| when | 2015 |
| where | Salt Lake City, Utah |
| venue | Summer institute in algebraic geometry, University of Utah |
| links | poster |
This talk was based on Covers of stacky curves and limits of plane quintics.
Syzygies of canonical curves and the geometry of \(\overline M_g\)
| when | 2015 |
| where | Daejeon, South Korea |
| venue | SIAM applied algebraic geometry conference |
| links | notes |
This talk was based on Toward GIT stability of syzygies of canonical curves.
GIT stability of syzygies of curves
| when | 2015 |
| where | Oberwolfach, Germany |
| venue | Classical Algebraic Geometry, Mathematisches Forschungsinstitut Oberwolfach |
| comments | mini talk |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Syzygies, GIT, and the moduli space of curves
| when | 2015 |
| where | West Lafayette, Indiana |
| venue | Purdue University |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Limits of plane curves via stacky branched covers
| when | 2015 |
| where | Columbus, Ohio |
| venue | Ohio State University |
This talk was based on Covers of stacky curves and limits of plane quintics.
Syzygies, GIT, and the log minimal model program for \(\overline{M}_g\)
| when | 2015 |
| where | Cambridge, Massachusetts |
| venue | Harvard University |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Picard groups of Hurwitz spaces
| when | 2015 |
| where | New York City, New York |
| venue | Courant Institute, New York University |
This talk was based on The Picard rank conjecture for the Hurwitz spaces of degree up to five.
The birational geometry of \(\overline M_g\)
| when | 2015 |
| where | Pune, India |
| venue | Indian Institute for Science Research and Education |
Syzygies of canonical curves and birational geometry of \(\overline M_g\)
| when | 2015 |
| where | Stony Brook, New York |
| venue | Stony Brook University |
This talk was based on Toward GIT stability of syzygies of canonical curves.
GIT stability of syzygies of canonical curves
| when | 2014 |
| where | Ann Arbor, Michigan |
| venue | University of Michigan |
This talk was based on Toward GIT stability of syzygies of canonical curves.
GIT stability of syzygies of canonical curves
| when | 2014 |
| where | New Haven, Connecticut |
| venue | Yale University |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Towards GIT stability of syzygies of canonical curves
| when | 2014 |
| where | Boston, Massachusetts |
| venue | Boston College |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Towards GIT stability of syzygies of canonical curves
| when | 2013 |
| where | Pohang, Korea |
| venue | Postech |
| links | notes |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Towards GIT stability of syzygies of canonical curves
| when | 2013 |
| where | Philadelphia, Pennsylvania |
| venue | Geometry of algebraic varieties, AMS sectional meeting |
This talk was based on Toward GIT stability of syzygies of canonical curves.
Sharp slope bounds for sweeping families of trigonal curves
| when | 2013 |
| where | Boston, Massachusetts |
| venue | Algebraic geometry northeastern series, Boston College |
| links | poster |
This talk was based on Sharp slope bounds for sweeping families of trigonal curves.
Alternate compactifications of Hurwitz spaces
| when | 2013 |
| where | Palo Alto, California |
| venue | Stanford University |
| links | notes |
This talk was based on Alternate compactifications of Hurwitz spaces.
Compactifying spaces of branched covers
| when | 2013 |
| where | Princeton, New Jersey |
| venue | Princeton University |
This talk was based on Alternate compactifications of Hurwitz spaces.
Alternate compactifications of Hurwitz spaces
| when | 2012 |
| where | Houston, Texas |
| venue | Rice University |
This talk was based on Alternate compactifications of Hurwitz spaces.
Compactifications of Hurwitz spaces
| when | 2011 |
| where | Cambridge, Massachusetts |
| venue | Massachusetts Institute of Technology |
| links | notes |
This talk was based on Alternate compactifications of Hurwitz spaces.
Compactifications of Hurwitz spaces
| when | 2011 |
| where | New York City, New York |
| venue | Columbia University |
This talk was based on Alternate compactifications of Hurwitz spaces.
Compactifications of Hurwitz spaces
| when | 2011 |
| where | Stony Brook, New York |
| venue | Stony Brook University |
This talk was based on Alternate compactifications of Hurwitz spaces.
Compactifications of Hurwitz spaces
| when | 2011 |
| where | Providence, Rhode Island |
| venue | Brown University |
This talk was based on Alternate compactifications of Hurwitz spaces.
Birational geometry of the space of marked trigonal curves
| when | 2011 |
| where | Cambridge, Massachusetts |
| venue | A celebration of algebraic geometry: a conference for the 60th birthday of Joe Harris, Harvard University |
| comments | poster |
| links | poster |
This talk was based on Modular compactifications of the space of marked trigonal curves.