Events
| << Prev | October 06, 2008 - October 13, 2008 | Next >> |
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Mon 10/6
The Descent Construction for Essentially Self-Dual Representations (Number Theory Seminar)
Joseph Hundley (Southern Illinois Universtity, Carbondale)
Start: 4:30 pm
End: 5:30 pm
Location: MW 154
MW 154
We describe an extension of the Ginzburg-Rallis-Soudry descent construction
from self-dual representations to those which are only "essentially" self
dual, i.e., isomorphic to some twist of their own contragredients. This
provides a complement to recent work of Asgari-Shahidi on functorial
transfer from GSpin groups to general linear groups, as well as work of
Asgari-Raghuram on a cuspidality criterion for the exterior square lift from
GL(4) to GL(6).
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Tue 10/7
Epsilon-independence between two processes (Ergodic Theory and Probability Seminar)
Paulina Grzegorek (Wroclaw)
Start: 2:30 pm
End: 3:30 pm
Location: TBA
TBA
We have a standard measure preserving invertible transformation. We use
the language of entropy to study the notion of epsilon-independence of a
process as well as between two processes generated on the transformation by
finite (or countable) measurable partitions.
A representation-theoretic study of the coordinate ring of eight ordered points on the line (Algebraic Geometry Seminar)
Benjamin Howard (University of Michigan)
Start: 4:30 pm
End: 5:30 pm
Location: Cockins Hall 240 (MBI lecture hall)
Cockins Hall 240 (MBI lecture hall)
The projective coordinate ring of the moduli space M_8 of
eight ordered points on the line is a quotient of Sym(V) by an ideal I, where V
is an irreducible fourteen-dimensional representation of the symmetric group
S_8. We show that there is a unique cubic hypersurface S in projective space
P(V) which is stable under S_8, whose equation s is skew-invariant, and that
the singular locus of S is the modular fivefold M_8. In characteristic zero, we
prove (without a computer) via commutative algebra and representation theory,
that the (fourteen) partial derivatives of s generate the ideal I, and we find
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Wed 10/8
Children's Drawings and Subgroups of PSL(2, Z) (Graduate Student Seminar on Number Theory)
erica j. Whitaker
Start: 4:30 pm
Location: CH 228
CH 228
Grothendieck's "dessins d'enfants" can be thought of as connected bipartite graphs together with an ordering of the edges at each vertex. There is a correspondence between a certain class of dessins and finite-index subgroups of PSL(2, Z), and also a correspondence between all dessins and finite-index subgroups of Γ(2), a subgroup of PSL(2, Z). We will look at examples of dessins and subgroups and the correspondence between them. We will also talk about congruence versus noncongruence subgroups and how the dessins can help us distinguish between these. (This talk will be introductory and expository.)
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Thu 10/9
Expansions of the real field by sets of natural numbers (Logic Seminar)
Chris Miller (OSU)
Start: 3:30 pm
End: 4:30 pm
Location: SO 44
SO 44
I will survey the question: What can be said about expansions of the field of real numbers by sets of natural numbers? In particular, under what circumstances is N definable, and what can be said if N is not definable?
János Kollár (Princeton University)
Start: 4:30 pm
End: 5:30 pm
Location: MA240
MA240
The simplest Cremona transformation of projective 3-space is the | ||
Fri 10/10
Extended Picard complexes and linear algebraic groups (Arithmetic Geometry Seminar)
Mikhail Borovoi (Tel-Aviv University)
Start: 2:30 pm
End: 3:30 pm
Location: MW 154
MW 154
Inspired by a work of Kottwitz, we introduce a complex UPic(X),
which is useful when computing the Picard group and the algebraic Brauer group of a geometrically irreducible variety X over a field k of characteristic 0 which is not necessarily algebraically closed. We compute this complex UPic(X) up to an isomorphism in the derived category when X is a linear algebraic group or a homogeneous space. This is a joint work with the late Joost van Hamel. This will be a talk on algebraic groups. I shall assume that the listeners know what is a maximal torus of a reductive group and | ||
Sat 10/11
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Sun 10/12
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Mon 10/13
Symmetries and Zeroes (Number Theory Seminar)
David Goss (OSU)
Start: 4:30 pm
End: 5:30 pm
Location: MW 154
MW 154
It is well known that Euler experimentally discovered the functional equation of the Riemann zeta function. Indeed he detected the fundamental $s\mapsto 1-s$ invariance of $\zeta(s)$ by looking only at special values. In particular, via this functional equation, $\Z/(2)$ is realized as a group of symmetries of $\zeta(s)$. If one includes complex conjugation, one then has a group of symmetries of $\zeta(s)$ of order $4$. In this paper, we use the theory of special-values of our characteristic $p$ zeta functions to experimentally detect a natural symmetry group for these functions of cardinality ${\mathfrak c}=2^{\aleph_0}$ (where $\mathfrak c$ is the cardinality of the continuum). This group appears as homeomorphisms of $\Zp$ which stabilize both the positive and negative integers. The exact form that these symmetries will ultimately take is not known at this time. We discuss all of this as well as some indications of similar phenomena classically.
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