Dennis Gaitsgory
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Dennis Gaitsgory has a total of 24 co-authors. Here are the top co-authors by number of shared publications:
- Edward Frenkel
Department of Mathematics, University of California, Berkeley, USA
7 shared publications - Ivan Mirković
Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, USA
5 shared publications - Alexander Braverman
Department of Mathematics Brown University 151 Thayer St. 02912 Providence RI USA
4 shared publications - Michael Finkelberg
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
4 shared publications A. Braverman
Department of Mathematics, MIT, Cambridge MA 02139, USA US
3 shared publications- Dima Arinkin
Mathematics Department University of Wisconsin-Madison 480 Lincoln Drive 53706 Madison WI USA
3 shared publications
Latest Publications
- Open Access
Intersection cohomology of Drinfeld's compactifications
Let $X$ be a smooth complete curve, $G$ be a reductive group and $P\subset G$ a parabolic. Following Drinfeld, one defines a compactification $\widetilde{\on{Bun}}_P$ of the moduli stack of $P$-bundles on $X$. The present paper is concerned with the explicit description of the Intersection Cohomology sheaf of $\widetilde{\on{Bun}}_P$. The description is given in terms of the combinatorics of the Langlands dual Lie algebra $\check{\mathfrak g}$.Open AccessIntersection cohomology of Drinfeld's compactifications
Let $X$ be a smooth complete curve, $G$ be a reductive group and $P\subset G$ a parabolic. Following Drinfeld, one defines a compactification $\widetilde{\on{Bun}}_P$ of the moduli stack of $P$-bundles on $X$. The present paper is concerned with the explicit description of the Intersection Cohomology sheaf of $\widetilde{\on{Bun}}_P$. The description is given in terms of the combinatorics of the Langlands dual Lie algebra $\check{\mathfrak g}$. - 1 January 2020
- Published by International Press of Boston in Pure and Applied Mathematics Quarterly
- Vol. 16 (3) , 775-904
The local and global versions of the Whittaker category
- 1 January 2020
- Published by International Press of Boston in Pure and Applied Mathematics Quarterly
- Vol. 16 (3) , 775-904
The local and global versions of the Whittaker category
- Open Access
An Iwahori-Whittaker model for the Satake category
In this paper we prove, for G a connected reductive algebraic group satisfying a technical assumption, that the Satake category of G (with coefficients in a finite field, a finite extension of Q_l, or the ring of integers of such a field) can be described via Iwahori-Whittaker perverse sheaves on the affine Grassmannian. As an application, we confirm a conjecture of Juteau-Mautner-Williamson describing the tilting objects in the Satake category.
Open AccessAn Iwahori-Whittaker model for the Satake category
In this paper we prove, for G a connected reductive algebraic group satisfying a technical assumption, that the Satake category of G (with coefficients in a finite field, a finite extension of Q_l, or the ring of integers of such a field) can be described via Iwahori-Whittaker perverse sheaves on the affine Grassmannian. As an application, we confirm a conjecture of Juteau-Mautner-Williamson describing the tilting objects in the Satake category.
- 16 February 2018
- Published by Springer Nature in Selecta Mathematica
- Vol. 24 (1) , 1-5
A tribute to Sasha Beilinson
- 16 February 2018
- Published by Springer Nature in Selecta Mathematica
- Vol. 24 (1) , 1-5
A tribute to Sasha Beilinson
- Open Access
- 8 May 2017
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 31 (1) , 135-214
The category of singularities as a crystal and global Springer fibers
We prove the “gluing conjecture” on the spectral side of the categorical geometric Langlands conjecture. The key tool is the structure of crystal on the category of singularities, which allows one to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.
- 8 May 2017
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 31 (1) , 135-214
Open AccessThe category of singularities as a crystal and global Springer fibers
We prove the “gluing conjecture” on the spectral side of the categorical geometric Langlands conjecture. The key tool is the structure of crystal on the category of singularities, which allows one to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.
- Open Access
The category of singularities as a crystal and global Springer fibers
We prove the "Gluing Conjecture" on the spectral side of the categorical geometric Langlands correspondence. The key tool is the structure of crystal on the category of singularities, which allows to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.
Open AccessThe category of singularities as a crystal and global Springer fibers
We prove the "Gluing Conjecture" on the spectral side of the categorical geometric Langlands correspondence. The key tool is the structure of crystal on the category of singularities, which allows to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.
- 1 October 2016
- Published by Springer Nature in Selecta Mathematica
- Vol. 22 (4) , 1793-1795
The Mathematics of Joseph Bernstein
- 1 October 2016
- Published by Springer Nature in Selecta Mathematica
- Vol. 22 (4) , 1793-1795
The Mathematics of Joseph Bernstein
- Open Access
Acyclic complexes and 1-affineness
This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups and affine spaces that may be of independent interest.
Open AccessAcyclic complexes and 1-affineness
This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups and affine spaces that may be of independent interest.
- Open Access
Singular support of coherent sheaves, and the geometric Langlands conjecture
We develop the notion of singular support of a coherent sheaf on a quasi-smooth DG scheme or stack and use it to formulate the Geometric Langlands Conjecture.
Open AccessSingular support of coherent sheaves, and the geometric Langlands conjecture
We develop the notion of singular support of a coherent sheaf on a quasi-smooth DG scheme or stack and use it to formulate the Geometric Langlands Conjecture.
- Open Access
Sheaves of categories and the notion of 1-affineness
We define the notion of 1-affineness for a prestack, and prove an array of results that establish 1-affineness of certain types of prestacks.
Open AccessSheaves of categories and the notion of 1-affineness
We define the notion of 1-affineness for a prestack, and prove an array of results that establish 1-affineness of certain types of prestacks.