Representation Theory Seminar
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Thu, 13/10/2011 15:00 |
Petter Bergh (Trondheim) |
Representation Theory Seminar  |
L3 |
| This is based on joint work with Dave Jorgensen. Given a Gorenstein algebra, one can define Tate-Hochschild cohomology groups. These are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild cohomology groups for all degrees larger than the injective dimension of the algebra. We prove certain duality theorems relating the cohomology groups in positive degree to those in negative degree, in the case where the algebra is Frobenius (for example symmetric). We explicitly compute all Tate-Hochschild cohomology groups for certain classes of Frobenius algebras, namely, certain quantum complete intersections. | |||
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Thu, 27/10/2011 14:00 |
Andrzej Skowronski (Torun) |
Representation Theory Seminar |
L3 |
| The class of finite dimensional algebras over an algebraically closed field K may be divided into two disjoint subclasses (tame and wild dichotomy). One class consists of the tame algebras for which the indecomposable modules occur, in each dimension d, in a finite number of discrete and a finite number of one-parameter families. The second class is formed by the wild algebras whose representation theory comprises the representation theories of all finite dimensional algebras over K. Hence, the classification of the finite dimensional modules is feasible only for the tame algebras. Frequently, applying deformations and covering techniques, we may reduce the study of modules over tame algebras to that for the corresponding simply connected tame algebras. We shall discuss the problem concerning connection between the tameness of simply connected algebras and the weak nonnegativity of the associated Tits quadratic forms, raised in 1975 by Sheila Brenner. | |||
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Thu, 10/11/2011 14:00 |
Prof D. Arinkin |
Representation Theory Seminar |
L3 |
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Thu, 24/11/2011 14:00 |
Ivan Fesenko (University of Nottingham) |
Representation Theory Seminar |
L3 |
| I will discuss some of new concepts and objects of two-dimensional number theory: how the same object can be studied via low dimensional noncommutative theories or higher dimensional commutative ones, what is higher Haar measure and harmonic analysis and how they can be used in representation theory of non locally compact groups such as loop groups and Kac-Moody groups, how classical notions split into two different notions on surfaces on the example of adelic structures, what is the analogue of the double quotient of adeles on surfaces and how one could approach automorphic functions in geometric dimension two. | |||
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Thu, 01/12/2011 15:00 |
Kobi Kremnitzer (Oxford) |
Representation Theory Seminar |
L3 |
| I'll present the work of Gaitsgory arXiv:1108.1741. In it he uses Beilinson-Drinfeld factorization techniques in order to uniformize the moduli stack of G-bundles on a curve. The main difference with the gauge theoretic technique is that the the affine Grassmannian is far from being contractible but the fibers of the map to Bun(G) are contractible. | |||
