Publications

Preprints

• A support theorem for the Hitchin fibration: the case of GL_n and K_C (with M. de Cataldo and L. Migliorini, preprint 2019)
• Cartan--Iwahori--Matsumoto decompositions for reductive groups (with J. Alper and D. Halpern-Leistner, preprint 2019)
• Existence of moduli spaces for algebraic stacks (with J. Alper and D. Halpern-Leistner, preprint - update 6.5.2019)

Articles

• Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles (with S. Bradlow, O. Garcia-Prada, P. Gothen, preprint, in Geometry and Physics Vol 2, A Festschrift in honour of Nigel Hitchin 2018)
• Langlands parameterization over function fields following V. Lafforgue. (Notes for an introductory talk given at VIASM. Acta Mathematica Vietnamica, 43(1) (2018), 45-66)
• Hilbert-Mumford stability on algebraic stacks and applications to G-bundles on curves. (preliminary version revised on 12.7.2017,  EPIGA Volume 1 (2017))
• The intersection form on moduli spaces of twisted PGL_n Higgs bundles vanishes, (preprint, Math. Ann. 365 (2016) no. 3-4 1499-1526).
• A conjecture of Hausel on the moduli space of Higgs bundles on a curve. (survey based on a talk at conference for G. Laumon,  Astérisque No. 370 (2015), 157–175 in "De la géométrie algébrique aux formes automophes (I) une collection d'articles en l'honneur du soixantième anniversaire de Gérard Laumon")).
• The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n) (with O. García-Prada, Duke Math. J. 162 (2013) 2731-2749, preprint pdf)
• Cohomology of the moduli stack of coherent sheaves on a curve (in Geomtry and Arithmetic, EMS, preprint pdf)
• On the motive of moduli spaces of chains and Higgs bundles (with O. García-Prada and A. Schmitt, to appear in JEMS Vol 16 (2014), preprint pdf)
• Kloosterman sheaves for reductive groups (with Ngo Bao Chau and Zhiwei Yun, preprint pdf, Annals of Mathematics 177 (2013), 241-310)
• Addendum to "Semistable reduction for G-bundles on curves." (J. Alg. Geom. 19 (2010), 193-197, preprint, pdf)
• Lectures on the moduli stack of vector bundles on a curve (in: Affine Flag Manifolds and Principal Bundles, Trends in Mathematics, Birkhäser 2010, preprint, pdf)
• The bigger Brauer group and twisted sheaves. (with S. Schröer, J. Algebra 322 (2009), 1187-1195, preprintpdf)
• Uniformization of $\mathcal{G}$-bundles. (Math. Ann. 347 (3) (2010) (open access), preprint pdf, revised version September 2009)
• Bounds for Behrend's conjecture on the canonical reduction. (Int. Math. Res. Notices 2008, article ID rnn045-17, corrected preprint version pdf)
• The cohomology ring of moduli stacks of principal bundles over curves. (with A. Schmitt, Documenta Mathematica 15 (2010), preprint version pdf)
• Semistable reduction for G-bundles on curves. (pdf J. Alg. Geom. 17 (2008), 167-183)
• Twisted Chern Classes and G_m-gerbes, Comptes Rendus 341, 10 (2005), 623-626 (preliminary version pdf)
• Notes on differentiable stacks: Notes of two talks given at the Forschungsseminar Bunke-Schick, that were meant to give an introduction to differentiable stacks.(pdf), Mathematisches Institut Universität Göttingen,Seminars 2004/05 , Universitätsverlag Göttingen (2005), 1-32
• Dissertation: Coherent sheaves with parabolic structures and construction of Hecke eigensheaves for some ramified local systems (pdf), Ann. Inst. Fourier 54, 7 (2004), 2235-2325.
• Wenig verzweigte geometrische Langlands--Korrespondenz, Mathematisches Institut, Universität Göttingen, ( Seminars 2003/04 , Universitätsverlag Göttingen (2004), 127-135
• Diplomarbeit: Über den Modulstack der Vektorbündel auf Kurven (dvi)