# Experience

September 2017 – Present
Vienna

#### Faculty of Mathematics, University of Vienna

September 2016 – August 2017
Klosterneuburg

#### Institute of Science and Technology Austria (ISTA)

September 2015 – August 2016
Trieste

#### Scuola Internazionale Superiore di Studi Avanzati (SISSA)

February 2013 – August 2015
Trieste

#### International Center for Theoretical Physics (ICTP)

October 2012 – December 2012
Moscow

#### Higher School of Economics

October 2010 – September 2012
Cologne

#### University of Cologne

September 2009 – September 2010
Bonn

#### Hausdorff Center for Mathematics

September 2008 – August 2009
Bonn

# Selected Publications

. Poincare polynomials of character varieties, Macdonald polynomials and affine Springer fibers. arXiv preprint arXiv:1710.04513, accepted in Ann. of Math., 2020.

. Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures). Invent. Math. DOI: 10.1007/s00222-020-00950-1, 2020.

. The $A_{q,t}$ algebra and parabolic flag Hilbert schemes. Math. Ann. DOI: 10.1007/s00208-019-01898-1, 2019.

. Integrality of Hausel–Letellier–Villegas kernels. Duke Math. J. 167 (2018), no. 17, 3171–3205, 2018.

. A proof of the shuffle conjecture. J. Amer. Math. Soc. 31 (2018), no. 3, 661–697, 2017.

. Finite hypergeometric functions. Pure Appl. Math. Q. 11 (2015), no. 4, 559–589, 2015.

. Derived categories of Keum's fake projective planes. Adv. Math. 278 (2015), 238–253, 2015.

. Dubrovin's conjecture for IG(2,6). Int. Math. Res. Not. IMRN 2015, no. 18, 8847–8859, 2014.

# Recent Publications

. Poincare polynomials of character varieties, Macdonald polynomials and affine Springer fibers. arXiv preprint arXiv:1710.04513, accepted in Ann. of Math., 2020.

. Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures). Invent. Math. DOI: 10.1007/s00222-020-00950-1, 2020.

. $\mathbb{Z}R$ and rings of Witt vectors $W_S(R)$. Rend. Semin. Mat. Univ. Padova 142 (2019), 93–102, 2019.

. Cell decompositions of character varieties. arXiv preprint arXiv:1905.10685, 2019.

. Elliptic dilogarithms and parallel lines. J. Number Theory 204 (2019), 1–24, 2019.

. On quantum cohomology of Grassmannians of isotropic lines, unfoldings of $A_n$-singularities, and Lefschetz exceptional collections. Ann. Inst. Fourier (Grenoble) 69 (2019), no. 3, 955–991, 2019.

. Rationality proofs by curve counting. Experimental Mathematics DOI: 10.1080/10586458.2019.1691088, 2019.

. Serre duality for Khovanov-Rozansky homology. Selecta Math. (N.S.) 25 (2019), no. 5, Art. 79, 33 pp., 2019.

. The $A_{q,t}$ algebra and parabolic flag Hilbert schemes. Math. Ann. DOI: 10.1007/s00208-019-01898-1, 2019.

. The Tutte polynomial and toric Nakajima quiver varieties. arXiv preprint arXiv:1910.01633, 2019.

# Recent & Upcoming Talks

Five-term relations
Mar 11, 2019 4:00 PM

# Projects

#### Macdonald polynomials and related structures in geometry

FWF Standalone Project