Ronno Das
he/him/his · রণ্ব দাস · ɹɒn.noʊ ðɑːʃ
I am a topologist, specifically interested in the topology of moduli spaces, in particular configuration spaces and spaces of maps.
More details are in my CV.
updates
current
I am a postdoc at Stockholm University and can be regularly found in office B1370. Dan Petersen is my postdoc mentor.
teaching
TA for MM7052 Topology (course webpage)
taught by Jonas Bergström
exercise sessions on Mondays 14:00–15:00
contact

ronnodas@gmail.com 

ronno.das@math.su.se 

Matematiska institutionen 106 91 Stockholm 

+1 8722228576 
publications

Homology of spaces of curves on blowups
with Philip Tosteson
2024 · arxivabstract
We consider the space of holomorphic maps from a compact Riemann surface to a projective space blown up at finitely many points. We show that the homology of this mapping space equals that of the space of continuous maps that intersect the exceptional divisors positively, once the degree of the maps is sufficiently positive compared to the degree of homology. The proof uses a version of Vassiliev's method of simplicial resolution. As a consequence, we obtain a homological stability result for rational curves on the degree \(5\) del Pezzo surface, which is analogous to a case of the Batyrev–Manin conjectures on rational point counts.

The Mumford conjecture (after Bianchi)
with Dan Petersen
2024 · arxivabstract
We give a selfcontained and streamlined rendition of Andrea Bianchi's recent proof of the Mumford conjecture using moduli spaces of branched covers.

Homological stability for the space of hypersurfaces with marked points
with Alexis Aumonier
2023 · arxivabstract
We study the space of marked smooth hypersurfaces in a given linear system. Specifically, we prove a homology hprinciple to compare it with a space of sections of an appropriate jet bundle. Using rational models, we compute its rational cohomology in a range of degrees, and deduce a homological stability result for hypersurfaces of increasing degree. We also describe the Hodge weights on the stable cohomology, and thereby connect our topological result to motivic results of Howe.

Cohomological and motivic inclusionexclusion
with Sean Howe
2024 · Compositio Mathematica, 160, 9, pp. 2228–2283
journal · arxivabstract
We categorify the inclusionexclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two spectral sequences of a stratified space and certain Vassilievtype spectral sequences; we also obtain Euler characteristic analogs in the Grothendieck ring of varieties. As an application, we give an algebrogeometric proof of Vakil and Wood's homological stability conjecture for the space of smooth hypersurface sections of a smooth projective variety. In characteristic zero this conjecture was previously established by Aumonier via topological methods.

Zeta statistics and Hadamard functions
with Margaret Bilu and Sean Howe
2022 · Advances in Mathematics, 407
journal · arxivabstract
We introduce the notion of 'Hadamard convergence' for zeta functions of a family of algebraic varieties. This is stronger than both convergence of point counts over finite fields and convergence in dimension of clases in a suitable Grothendieck ring. We make the metaconjecture that any 'natural' sequence of zeta functions which converges to a Hadamard function in both the weight and pointcounting topologies converges also in the Hadamard topology. For statistics arising from Bertini problems, zerocycles or the BatyrevManin conjecture, this yields an explicit conjectural unification of existing results in motivic and arithmetic statistics that were previously connected only by analogy. As evidence for our conjectures, we show that Hadamard convergence holds for many natural statistics arising from zerocycles, as well as for the motivic height zeta function associated to the motivic BatyrevManin problem for split toric varieties.

Cohomology of the universal smooth cubic surface
2021 · The Quarterly Journal of Mathematics, 72, 3, pp. 795–815
journal · arxivabstract
We compute the rational cohomology of the universal family of smooth cubic surfaces using Vassiliev's method of simplicial resolution. Modulo embedding, the universal family has cohomology isomorphic to that of \(\mathbb{P}^2\). A consequence of our theorem is that over the finite field of order \(q\), away from finitely many characteristics, the average number of points on a smooth cubic surface is \(q^2 + q + 1\).

The space of cubic surfaces equipped with a line
2021 · Mathematische Zeitschrift, 298(1), pp. 653–670
journal · arxivabstract
The Cayley–Salmon theorem implies the existence of a 27sheeted covering space parametrizing the lines contained in smooth cubic surfaces over complex numbers. We compute the rational cohomology of the total space of this cover, using the spectral sequence in the method of simplicial resolution developed by Vassiliev. The covering map is an isomorphism in cohomology (in fact of mixed Hodge structures) and the cohomology ring is isomorphic to that of \(PGL(4,\mathbb{C})\). We derive as a consequence of our theorem that over the finite field of order \(q\) the average number of lines on a cubic surface equals 1 (away from finitely many characteristics); a priori this average is \(1 + O(q^{1/2})\) by a standard application of the Weil conjectures.

Configurations of noncollinear points in the projective plane
with Ben O'Connor
2021 · Algebraic and Geometric Topology, 21(4), pp. 1941–1972
journal · arxivabstract
We consider the space \(F_n\) of configurations of \(n\) points in \(P^2\) satisfying the condition that no three of the points lie on a line. For \(n = 4, 5, 6\), we compute \(H^*(F_n; \mathbb{Q})\) as an \(S_n\)representation. The cases \(n = 5, 6\) are computed via the Grothendieck–Lefschetz trace formula in étale cohomology and certain 'twisted' point counts for analogous spaces over \(\mathbb{F}_q\).

Arithmetic statistics on cubic surfaces
2020 · Research in the Mathematical Sciences, 7(3), p. 23
journal · arxivabstract
We compute the distributions of various markings on smooth cubic surfaces defined over a finite field, for example the distribution of pairs of points, 'tritangents' or 'double sixes'. We also compute the (rational) cohomology of associated bundles and covers over complex numbers.

Coxeter transformation groups and reflection arrangements in smooth manifolds
with Priyavrat Deshpande
2016 · Journal of Homotopy and Related Structures, 11(3), pp. 571–597
journal · arxivabstract
We prove a version of Salvetti's theorems for Coxeter groups acting on manifolds with each reflection fixing a codimension\(1\) submanifold. Then the fundamental groups of the tangent bundle complement and its quotient by the Coxeter group serve as the analogue of the (pure) Artin group. We construct a combinatorial cell complex which is equivariantly homotopy equivalent to the tangent bundle complement.
talks
Hypersurfaces and inclusionexclusion

24 Oct 2023 · Topology seminar · Florida State University

28 Jun 2023 · Mathematics Seminar · Chennai Mathematical Institute

2 Nov 2022 · Mathematics and Applied Mathematics seminar · Mälardalens University, Västerås
Cohomological and motivic inclusionexclusion

3 Mar 2022 · Algebraic Geometry and Number Theory Seminar · IST Austria
Stability of zeta statistics

26 Nov 2021 · Algebraic Geometry Seminar · Tata Institute of Fundamental Research

15 Jan 2021 · Algebra/Topology Seminar · University of Copenhagen

17 Nov 2020 · Algebra & Geometry Seminar · Stockholm University + KTH Royal Institute of Technology
Noncollinear points in the projective plane
Points and lines on cubic surfaces

7 Dec 2022 · Mathematics Colloquium · Kuwait University

9 Feb 2021 · Algebra, Geometry and Number Theory seminar · University of Bath

9 Nov 2019 · Special Session on Arithmetic Geometry in Finite Characteristic · AMS Sectional at University of California, Riverside

16 Sep 2019 · Number Theory Seminar · University of Utah

14 Sep 2019 · Special Session on Geometry and Topology in Arithmetic · AMS Sectional at University of Wisconsin–Madison

10 Jun 2019 · Workshop on Arithmetic Topology · PIMS, University of British Columbia · slides

19 Apr 2019 · Algebraic Geometry Seminar · Stanford University

29 Mar 2019 · Geometric Topology Seminar · Columbia University

17 Mar 2019 · Midwest Algebraic Geometry Graduate Conference · The University of Illinois at Chicago

20 Feb 2019 · lightning talk · Braids, Resolvent Degree and Hilbert’s 13th Problem Workshop · IPAM, University of California, Los Angeles · slides

6 Feb 2019 · Algebraic Geometry Seminar · The University of Illinois at Chicago
The space of cubic surfaces equipped with a line

13 Jun 2018 · lightning talk · Roots of Topology Workshop · University of Chicago · slides

8 Jun 2018 · Topology Students Workshop · Georgia Institute of Technology · slides

23 May 2018 · Algebraic Geometry Seminar · University of Chicago
Single cohomology classes in your area — this last weird trick will shock you!

23 Aug 2017 · colloquium · Chennai Mathematical Institute
Simplicial resolution a la Vassiliev and counting points

21 Aug 2017 · mathematics seminar · Chennai Mathematical Institute
Artin groups related to reflections on manifolds

11 Sep 2014 · research lecture series · Chennai Mathematical Institute · slides
other writing
doctoral thesis
Points and lines on cubic
surfaces
under Benson Farb
masters thesis
Salvetti complex construction for
manifold reflection arrangements
under Priyavrat Deshpande
notes
past teaching
courses taught
University of Chicago

2020 autumn · Calculus 1

2019 autumn · Calculus 2 (2 sections)

2018–19 · Elementary Functions and Calculus 1–3

2017–18 · Elementary Functions and Calculus 1–3
mentored REU students
University of Copenhagen

2022 summer · Andrei Staicu
University of Chicago

2019 summer · Jae Hee Lee, Khanh Pham, Tom Sawada, Edwin Suresh

2018 summer · Philip Adams, Alexander Burka, Spencer Dembner, William Garland, Xinyu Shi

2017 summer · Jackson Dougherty, Jasmine Katz, Anubhav Nanavaty

2016 summer · Mayanka Dutta, Julian Salazar, Hannah Santa Cruz, Squid TamarMattis
et cetera
tshirt designs
most of my tshirts are of my own design, though the jokes are often not original
I use spreadshirt for the actual printing
png files with background · email me for printingfriendly
versions
thesis defense crossword
beer skits
annual comedy show written and performed by the second year graduate students at UChicago
YouTube playlist for
beer skits 2017