Experience

 
 
 
 
 
March 2025 – Present
Vienna

Full Professor

Faculty of Mathematics, University of Vienna

 
 
 
 
 
May 2021 – February 2025
Vienna

Associate Professor

Faculty of Mathematics, University of Vienna

 
 
 
 
 
September 2017 – April 2021
Vienna

Assistant Professor (tenure track)

Faculty of Mathematics, University of Vienna

 
 
 
 
 
September 2016 – August 2017
Klosterneuburg

Postdoc

Institute of Science and Technology Austria (ISTA)

 
 
 
 
 
September 2015 – August 2016
Trieste

Postdoc

Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 
 
 
 
 
February 2013 – August 2015
Trieste

Postdoc

International Center for Theoretical Physics (ICTP)

 
 
 
 
 
October 2012 – December 2012
Moscow

Guest Lecturer

Higher School of Economics

 
 
 
 
 
October 2010 – September 2012
Cologne

Postdoc

University of Cologne

 
 
 
 
 
September 2009 – September 2010
Bonn

Postdoc

Hausdorff Center for Mathematics

 
 
 
 
 
September 2008 – August 2009
Bonn

Postdoc

Max Planck Institute for Mathematics

Awards and distinctions

  • 2026 — Frontiers of Science Award
  • 2026 — Invited speaker at the International Congress of Mathematicians
  • 2024 — Invited speaker at the European Congress of Mathematics

Selected Publications

. Toric stratifications of character varieties. Publ. Math. IHÉS 142, 153–240, 2025.

Preprint

. Tautological classes and symmetry in Khovanov–Rozansky homology. Duke Math. J. 173, no. 13, 2481–2561, 2024.

Preprint DOI

. Toric braids and $(m,n)$-parking functions. Duke Math. J. 170, no. 18, 4123–4169, 2021.

Preprint

. Poincaré polynomials of character varieties, Macdonald polynomials and affine Springer fibers. Ann. of Math. (2) 192, no. 1, 165–228, 2020.

Preprint

. Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures). Invent. Math. 221, no. 1, 301–327, 2020.

Preprint DOI

. A proof of the shuffle conjecture. J. Amer. Math. Soc. 31, no. 3, 661–697, 2018.

Preprint DOI

Recent Publications

More Publications

. On Macdonald expansions of $q$-chromatic symmetric functions and the Stanley–Stembridge conjecture. J. reine angew. Math., Accepted, 2026.

Preprint

. Refined Verlinde and Segre formula for Hilbert schemes. Moduli, Accepted, 2026.

Preprint

. Coherent sheaves on surfaces, COHAs and deformed $W_{1+\infty}$-algebras. Moduli 3, e13, 2026.

Preprint DOI

. Cohomology rings of character varieties. European Congress of Mathematics, 637–663, 2026.

Preprint DOI

. Hard Lefschetz phenomena and Lie algebra actions in various contexts. Proceedings of the International Congress of Mathematicians 2026 4, 586–601, 2026.

DOI

. Tautological classes for $(n,n+1)$ torus knots. Preprint, 2026.

Preprint

. A combinatorial formula for the nabla operator. Compos. Math. 161, no. 4, 800–830, 2025.

Preprint DOI

. Toric stratifications of character varieties. Publ. Math. IHÉS 142, 153–240, 2025.

Preprint

. On the global dimension of Nakayama algebras. Preprint, 2025.

Preprint

. Symmetric and non-symmetric F-conjectures are equivalent. Preprint, 2025.

Preprint

Selected Talks

Hard Lefschetz phenomena and Lie algebra actions
2026
International Congress of Mathematicians (invited lecture)
Symmetric functions in geometry
2025
Developments in the Mathematical Sciences
Cohomology rings of character varieties
2024
European Congress of Mathematics (invited lecture)
Five-term relations
Mar 11, 2019 4:00 PM
University of Geneva

Recent Posts

1 min read

Projects

Refined invariants in combinatorics, low-dimensional topology and geometry of moduli spaces

ERC Consolidator Grant

Macdonald polynomials and related structures in geometry

FWF Standalone Project

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