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Mathematische Annalen, ISSN 0025-5831, 2018, Volume 373, Issue 3-4, pp. 1103 - 1133
The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of nxn Hermitian matrices, given the eigenvalues of the summands. The regular faces... 
MATHEMATICS | INVARIANT-THEORY
Journal Article
Journal of the American Mathematical Society, ISSN 0894-0347, 1/2008, Volume 21, Issue 1, pp. 235 - 258
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 10/2012, Volume 98, Issue 4, pp. 367 - 389
We prove that the vector bundles of conformal blocks, on suitable moduli spaces of genus zero curves with marked points, for arbitrary simple Lie algebras and... 
Non-abelian theta functions | Hitchin connection | KZ equations | Conformal blocks | Secondary | Primary | MATHEMATICS | ZERO | MATHEMATICS, APPLIED | KNIZHNIK-ZAMOLODCHIKOV EQUATIONS | PRODUCT | TENSOR CATEGORIES | Algebra
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2016, Volume 284, Issue 3-4, pp. 961 - 987
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00209-016-1682-1 By way of... 
Journal Article
Journal of the American Mathematical Society, ISSN 0894-0347, 4/2008, Volume 21, Issue 2, pp. 365 - 408
Journal Article
Journal of Differential Geometry, ISSN 0022-040X, 2009, Volume 82, Issue 2, pp. 445 - 465
For a compact Riemann surface X of positive genus, the space of sections of a certain theta bundle on moduli of bundles of rank r and level k admits a natural... 
MATHEMATICS | BUNDLES | LEVEL-RANK DUALITY | SPACES | WZW MODELS | VARIETIES | PICARD GROUP | CURVES | MODULI
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2016, Volume 284, Issue 3, pp. 961 - 987
By way of intersection theory on $$\overline{\mathcal {M}}_{g,n}$$ M ¯ g , n , we show that geometric interpretations for conformal blocks, as sections of... 
Mathematics, general | Mathematics
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2007, Volume 216, Issue 1, pp. 346 - 357
We give a geometric proof of a conjecture of Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for... 
Tensor product of representations | Grassmannians | Geometric invariant theory | grassmannians | MATHEMATICS | tenser product of representations | geometric invariant theory | HONEYCOMB MODEL
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2016, Volume 288, pp. 1309 - 1359
We construct deformations of the small quantum cohomology rings of homogeneous spaces , and obtain an irredundant set of inequalities determining the... 
Multiplicative eigenvalue problem | Quantum cohomology | Deformation theory | MATHEMATICS | GRASSMANNIANS | PARABOLIC G-BUNDLES | PRODUCTS | LINE | CURVES | MODULI SPACES | CONJECTURE
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 10/2006, Volume 166, Issue 1, pp. 185 - 228
Journal Article
ALGEBRAIC GEOMETRY, ISSN 2313-1691, 03/2019, Volume 6, Issue 2, pp. 234 - 259
We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial provided that the order of... 
conformal blocks | MATHEMATICS | B-reduction | principal bundles | singular curves | Drinfeld-Simpson theorem | MODULI
Journal Article
Compositio Mathematica, ISSN 0010-437X, 10/2001, Volume 129, Issue 1, pp. 67 - 86
I give the necessary and sufficient conditions for the existence of Unitary local systems with prescribed local monodromies on P1 − S where S is a finite set.... 
Harder–Narasimhan filtration | vector bundle | local systems | Mathematics, general | Mathematics | representations of fundamental groups | Klyachko's theorem | Local systems | Vector bundle | Harder-Narasimhan filtration | Representations of fundamental groups
Journal Article
Journal of Algebraic Geometry, ISSN 1056-3911, 2006, Volume 15, Issue 1, pp. 133 - 173
We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The... 
MATHEMATICS | EIGENVALUES | HERMITIAN MATRICES | SUMS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2012, Volume 354, Issue 2, pp. 401 - 425
We prove a generalization of Fulton’s conjecture which relates intersection theory on an arbitrary flag variety to invariant theory. 
Mathematics, general | 20G05 | Mathematics | 14C17 | 14L30
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2014, Volume 64, Issue 4, pp. 1669 - 1719
We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus 0 for classical Lie... 
Logarithmic forms | Singular cohomology | Conformal blocks | conformal blocks | MATHEMATICS | logarithmic forms | UNITARITY | HYPERPLANES | singular cohomology
Journal Article
Journal of Algebraic Geometry, ISSN 1056-3911, 2010, Volume 19, Issue 2, pp. 199 - 242
In this paper we consider the eigenvalue problem, intersection theory of homogeneous spaces (in particular, the Horn problem) and the saturation problem for... 
MATHEMATICS | EIGENVALUES | MODEL
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2012, Volume 354, Issue 2, pp. 401 - 425
We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory. 
MATHEMATICS | VARIETIES
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2004, Volume 2004, Issue 69, pp. 3709 - 3721
We give an algebro-geometric relation between intersection theory of Grassmannians and invariant theory of the general linear group. From points of... 
MATHEMATICS
Journal Article
05/2017
The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of $n\times n$ Hermitian matrices, given the eigenvalues of the summands. The... 
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 01/2004, Volume 2004, Issue 69, pp. 3709 - 3721
We give an algebro-geometric relation between intersection theory of Grassmannians and invariant theory of the general linear group. From points of... 
Journal Article
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