Algebra Seminar 2002-07
Fall Semester, 2007
September 19
Title: The
Steinberg Module and the Steinberg Tensor Product Theorem
Speaker: Chris Drupieski (UVa)
Title: Automorphisms of buildings and a lemma about Coxeter groups
Speaker: Peter Abramenko (UVa)
October 3
Title:
Toric
degeneration of
Bott-Samelson-Demazure-Hansen
Varieties
Speaker:
Paramasamy Karuppuchamy
(UVa)
October 10
Title: Representation
Theory of the Lie superalgebra of type C
Speaker:
Shun-Jen Cheng (Academia
Sinica, Taipei, Taiwan)
Title: The Feynman diagram calculus underlying Gordan's bases for covariants of binary forms
Speaker: Malek Abdesselam (UVa)
October 24 No Talk
October 31
Title: Representation
growth of compact p-adic Lie groups
Speaker: Benjamin Klopsch (Royal Holloway, University of London)
November 7
Title: The
classification of maximal graded subalgebras of affine Kac-Moody
algebras
or, the classification of maximal filtrations
in finite
dimensional simple Lie algebras
Speaker: Yiftach Barnea (Royal Holloway, University of London)
November 14
Title: The centers
of spin symmetric group algebras and Catalan numbers
Speaker: Jill (McCarthy) Tysse (UVa)
November 28
Title: Generic extension monoid algebras for cyclic quivers
Speaker: Bangming Deng (Beijing Normal University)
December 5
Title: Linear quivers, Generic extensions and Kashiwara operators
Speaker: Jie Du (UNSW, Australia)
Student presentations:
Jinkui Wan Nov. 27 & 29, Crystal basis for the basic representation
of affine sl_r
Lei Zhao, Dec. 3, Quantum groups
at roots of unity, I
Ta Khongsap, Dec. 4, R-matrix
and Schur-Jimbo duality
Chris Drupieski, Dec. 6, Quantum
groups at roots of unity, II
Spring Semester, 2007
January 17
Title: On the
structure of Kirillov-Reshetikhin
modules
Speaker: Adriano Adrega de Moura (University of Campinas, Brazil)
January 24
(job interviews)
No talk
Title: Representations of finite groups of Lie type in the defining characteristic
Speaker: Cornelius Pillen (University of South Alabama)
February 7 (job interviews) No talk
February 14
Title: Cohomology of Lie algebras and Frobenius kernels
Speaker: Chris Bendel (University of Wisconsin-Stout)
February 21
Title: Profinite trees
Speaker: Pavel Zalesskii (University of Brasilia, Brazil)
February 28
Title: Profinite trees II
Speaker: Pavel Zalesskii (University of Brasilia, Brazil)
March 7 (Spring break) No talk
March 14
Title: Projective modules for Chevalley groups and Frobenius kernels
Speaker: Dan Nakano (University of Georgia)
March 23-24, Friday and Saturday
Faulkner and Ward retirement conference
March 28
Title: A convexity theorem for affine buildings
Speaker: Petra Hitzelberger (Muenster, Germany)
April 2, Monday 3:30pm
Title: W-algebras and representations of affine Lie algebras at the critical level
Speaker: Tomoyuki Arakawa (Nara Women's University, Japan)
April 11
Title: Spin Hecke algebras of affine type
Speaker: Ta Khongsap (UVa)
April 18
Title: Dunkl operators and double affine Hecke algebras: a spin version
Speaker: Weiqiang Wang (UVa)
April 25
Title: Irreducible representations of finite and algebraic groups
Speaker: Leonard Scott (UVa)
May 2
Title: Modular representations of Lie superalgebras
Speaker: Lei Zhao (UVa)
-------------------------------------------------------------------
Fall
Semester, 2006
September 13
Speaker: Weiqiang Wang (UVa)
Title: On the work of Andrei
Okounkov, a Fields
medalist
September 20
Speaker: Terrell Hodge (Western Michigan
University)
Title: On
Nilpotent Orbits and Desingularizations of Their Closures
September 27
No talk
October 4
Speaker:
Ta Khongsap (UVa)
Title: On Hecke algebras of finite and affine
type
October 11
Speaker:
Paramasamy Karuppuchamy (UVa)
Title: Cohomology of line bundles on Schubert
varieties
October 18
Speaker: Weiqiang
Wang (UVa)
Title: Binary polyhedral
groups and (affine) Cartan matrices
October 25
Speaker: Tie Luo (NSF)
Title: Recent development in
holomorphic forms on algebraic varieties of general type
Speaker: Alexei Oblomkov (Princeton U.)
Title: Introduction into the Double Affine Hecke algebras
November 8
Speaker: Shun-Jen Cheng (Academia Sinica, Taipei)
Title: Kostant's homology formula for unitarizable gl_{\infty|\infty}-modules
November 15
Speaker: Chris Drupieski (UVa)
Title: Dynkin diagram automorphisms and twisted affine Kac-Moody algebras
November 23
Thanksgiving break, no talk
December 1, Friday (note the special day)
Speaker: V. Lakshmibai (Northeastern U.)
Title: Cohen-Macaulayness of certain rings of invariants
Abstract:
Let K be an algebraically closed field of characteristic different from 2.
We prove the First and Second Fundamental Theorems for the rings of invariants
for certain canonical actions of SL(n), SO(n) (with entries in K) on certain affine spaces.
As a consequence we prove the Cohen-Macaulayness of the corresponding rings of invariants.
As an application, we obtain a proof of the Cohen-Macaulayness of the moduli space of
equivalence classes of semi-stable rank 2, degree 0 vector bundles on a smooth projective curve.
December 13
Speaker: Richard Weiss (Tufts University)
Title: Jordan algebras and affine buildings of type (G_2)~
Abstract:
Moufang hexagons are the spherical buildings associated to
absolutely simple algebraic groups of relative type $G_2$. They are
classified by anisotropic cubic norm structures $(J,K,\#)$ in the
sense of Petersson and Racine. If $(J,K,\#)$ is an anisotropic CNS
and $K$ is complete with respect to a discrete valuation, then the
corresponding Moufang hexagon is the "building at infinity" of an
affine building of type $\tilde G_2$. We give a brief overview of
these remarkable objects and some of their principal features in
which several results of Petersson's (old and new) play a prominent role.
Some additional student presentations:
Speaker: Joe Johnson (UVa), 12/5/06
Title: Kostant homology and the BGG resolution
Speaker: Jinkui Wan (UVa)
Title: The fundamental modules of the classical simple Lie algebras
Speaker: Lei Zhao (UVa)
Title: The Harish-Chandra homomorphism
-
-------------------------------------------------------------
Spring Semester, 2006
February 1
Speaker:
John Faulkner
(UVA)
Title: Realization of graded-simple algebras as loop algebras
February 15
Speaker:
Jonathan Kujawa (University
of Georgia)
Title: An algebraist does knot theory
March 1
Speaker: Dijana Jakelic (UVA)
Title: Completions of crystal bases of some representations of
quantum groups
March 15
Speaker: Earl Taft (Rutgers)
Title: A class of left quantum groups
March 22
Speaker: Dave Taylor (UVA)
Title: Trace functions of integrable modules over classical
subalgebras of gl_\infty
March 29
Speaker: Igor Rapinchuk (Harvard)
Title: Algebraic and Analytic Aspects of Dirichlet's Prime Number
Theorem
March 31 (Friday), 3:30 pm
Speaker: Mikhail Ershov (IAS)
Title: Golod-Shafarevich groups with property (T ) and Kac-Moody
groups
April 5
No seminar
April 12
Speaker: Peter Abramenko (UVA)
Title: Affine BN-pairs for norm 1 groups of quaternion algebras
April 19
Speaker: Dan Nakano (University of
Georgia)
Title: Quantum group cohomology via the geometry of the nullcone
April 26
Speaker:
Tim Steger (Universita di
Sassari, IAS)
Title: Free Group Representations: Duplicity on the Boundary
May 3
Speaker: Sarah Bendall (UVA)
(student presentation)
Title: The conjugacy problem in Richard Thompson's group F (after
Kassabov-Matucci)
-
-------------------------------------------------------------
Fall Semester, 2005
August 31
Speaker: Aaron Phillips (UVA)
Title: The affine Hecke
algebra and friends.
Speaker: Dmitriy Sonkin (UVA)
Title: Graded diagrams method and the Burnside problem
September 14
Speaker: Weiqiang Wang (UVA)
Title: Introduction to a Fock space approach to the symmetric groups
September 21
Speaker: Jon Kujawa (University of Georgia)
Title: Cohomology and support
varieties for Lie superalgebras
Speaker: Nick Kuhn (UVA)
Title: Central extensions of finite groups and cohomology primitives
October 5, No Seminar.
October 12
Speaker: Kai-Uwe Bux (UVA)
Title: The Torelli group in Out(F_n) part II: geometric dimension
October 21
Speaker: Tom Haines (University of Maryland)
Title: The geometry of
convolution morphisms, and applications to saturation problems.
October 26
(student presentation)
Speaker: Lei Zhao (UVA)
Title: Representations of
finite-dimensional algebras via
quivers.
No talk.
November 9
(student presentations)
Speakers: Christopher Drupieski and Nicholas Hamblet (UVA)
Title: Division Algebra
Theorems of Frobenius and Wedderburn .
November 16
(student presentations)
(1) Speaker: Jason Castiglione (UVA)
Title: A simplicity
theorem for Tits systems.
(2) Speaker: Ta Khongsap (UVA)
Title: Irreducible
representations of the symmetric groups .
No talk (Thanksgiving break).
Student presentations:
--November 29
1) Speaker: Nan Lu (UVA)
Title: Introduction to division algebras .
2) Speaker: Ricardo Portilla (UVA)
Title: Polynomials over division rings .
--December 1
3) Speaker: Gregory Smith (UVA)
Title: Introduction to homological algebra .
4) Speaker: James Hughes (UVA)
Title: Hochschild homology .
--December 6
5) Speaker: Sarah Bendall (UVA)
Title: Classification of the finite subgroups of the rotation group .
-----------------------------------------------------------------------------
Spring Semester, 2005
January 26, Wednesday, 3:30
Speaker: Nanhua Xi (Academia Sinica, Beijing /UVA)
Title: The leading
coefficients of certain Kazhdan-Lusztig polynomials of the permutation
group S_n
February 2, Wednesday, 3:30,
Speaker: Bin Shu (ECNU, China /UVA)
Title: Finite Lie algebras
and their representations
Speaker: Dave Taylor (UVA)
Title: Trace Functions on Fock spaces and Howe duality
February 16, Wednesday, 3:30,
Speaker: Dijana Jakelic (UVA)
Title: Branched crystals and tensor products in category O
February 23, Wednesday, 3:30,
Speaker: Konstantin Styrkas (Yale)
Title: Regular representation on the big cell, Whittaker vectors, and projective modules in category O
March 3, Thursday, 4:00 (special day/time), joint seminar with Colloquium,
Speaker: John Thompson (Univ. Florida)
Title: Conjugacy classes in upper triangular groups
March 9, Wednesday, No Talk (Spring Break).
March 16, Wednesday, NO Talk this week.
March 23, Wednesday, 3:30,
Speaker: Andrei Rapinchuk (UVA)
Title: Normal subgroups of the multiplicative group of a division algebra, and valuations
March 25, FRIDAY, 3:30,
Speaker: Pierre-Emmanuel Caprace (Belgium)
Title: Rigidity of Coxeter groups
March 30, Wednesday, 3:30,
Speaker: Bangming Deng (Bejing Normal University/Kansas State University)
Title: Symplectic representations of a quiver
April 6, Wednesday, 3:30,
Speaker: Brian Kapp (UVA) (student presentation)
Title: The commutator group of the unitary group of a division algebra
April 13, Wednesday, 3:30,
Speaker: Kai-Uwe Bux (UVA)
Title: The Torelli Group in Out(F_n) (joint work with Mladen Bestvina and Dan Margalit)
April 20, Wednesday, 3:30, (Note: Olivier is also giving a colloquium talk this week)
Speaker: Olivier Schiffmann (ENS, France)
Title: Canonical bases and elliptic algebras
April 22, Friday, 3:30 (Student Presentations)
1) Speaker: Take Kaminogo
Title: Actions of groups on trees and amalgam presentations
2) Speaker: Christy Spofford
Title: The class number of an algebraic number field
April 27-28, "Symposium in honor of Charles Dunkl"
April 29, Friday, 3:30 (Student Presentations)
1) Speaker: Robert Allen
Title: Lie algebra cohomology
2) Speaker: Jessica Otis
Title: Pólya s Theory of Counting the Colorings of Unoriented Objects
3) Speaker: Mike Smith
Title: A realization of E_7 using the KKT construction
-----------------------------------------------------------------------------
Fall Semester, 2004.
September 3, Friday, 2pm
Peter Neumann (Queens College, Oxford): Orbital equations in
primitive permutation groups
September 8, Wednesday
Bangming Deng (Beijing Normal Univ.): Representations
of quivers with automorphism
September 15, Wednesday
Jie Du (Univ. of New South Wales, Australia): Infinitesimal quantum
gl_n and little q-Schur algebras
September 22, Wednesday
(student presentation)
Jill McCarthy(UVA): Quasi-hereditary
Algebras
October 6, Wednesday,
Semra Kaptanoglu (Middle East Technical U., Turkey): A detection theorem for Z/2 x Z/4-modules
October 13, Wednesday,
Herbert Abels (Univ. of Bielefeld, Germany): Geometry on linear groups: invariant metrics on reductive groups
October 20, Wednesday,
Kai-Uwe Bux (UVA): A geometric proof that SL_2(Z[t, t^{-1}]) is not finitely presented
October 27, Wednesday
Bangming Deng (Beijing Normal Univ.): Quantum Serre relations in Ringel-Hall algebras
November 3, Wednesday
Bin Shu (East China Normal Univ.): A survey of modular representations of simple Lie algebras, I
November 10, Wednesday
Bin Shu (East China Normal Univ.): A survey of modular representations of simple Lie algebras, II
November 19, Friday 4:30pm, Ker 326
Arun Ram (U. of Wisconsin-Madison): The form of theorems in combinatorial representation theory
(Note: Arun will be also giving a colloquium talk on Thursday, Nov. 18).
Nov. 24, Wednesday, No Seminar (due to Thanksgiving break)
Dec. 1, Wednesday (student presentation)
Wes Cramer (UVA), Advanced Kazhdan-Lusztig theory
Dec. 8, Wednesday (student presentation)
Wes Cramer (UVA), (More) Advanced Kazhdan-Lusztig theory
-
------------------------------------------------------------
Spring Semester, 2004.
January 21, 3:30 Wednesday,
Stephen Berman (
Saskatchewan,
Canada/UVa): Half-Lattice
VOA's
January 30, 3:30 Friday,
Jon Brundan (Oregon): Representations of shifted Yangians
February 6, 3:30 Friday
,
Antun Milas (RPI):
Modular Forms,
Partitions and Conformal Field Theory
February 11, 4:30 Wednesday,
Rui-bin Zhang (Univ. of Sydney, Australia):
Induced representations of the quantum general
linear supergroup and Bott-Borel-Weil theorem
February 18, 3:30 Wednesday,
no seminar.
March 1, 3, 5 (Monday, Wednesday, Friday),
3:30pm, Ker 317
Seok-Jin Kang (Korea Institute for Advanced Study
):
1) General theory of
crystal bases, Young tableaux and crystals,
2) Perfect crystals, paths, and combinatorics of Young walls,
3) Fock space representations of quantum affine algebras and
generalized Lascoux-Leclerc-Thibon algorithm
Jim Howland (UVA): Quantum mechanics for algebraists
March 24, 3:30 Wednesday,
Weiqiang Wang (UVA): Boson-Fermion correspondence and symmetric groups
March 31, 3:30 Wednesday (student presentation)
David Taylor (UVA): Schur-Howe duality and Gelfand-Tsetlin basis
April 9, 3:30 Friday
Bernard Leclerc (U. Caen, France): On the multiplicative structure of the dual canonical basis, II
April 14, 3:30 Wednesday
Arturo Pianzola (Alberta, Canada) : Twisted loop algebras and Serre's conjecture
April 21, 3:30 Wednesday (student presentation)
Brian Kapp (UVA): Constructions and counterexamples with twisted polynomial rings
April 23, 3:30 Friday (student presentation)
Jill McCarthy (UVA): Triangulated Categories
April 28, 3:30 Wednesday (student presentation)
Dominic Braun (UVA): Homotopy types of buildings
April 30, 3:30 Friday (student presentation)
Wes Cramer (UVA): The Steinberg tensor product theorem
May 7, 3:30 Friday (note the special day)
Hebing Rui (ECNU, Shanghai): Complex semisimple Brauer algebras
------------------------------------------------------------
Fall Semester, 2003
.
September 3
,
Wednesday
organizational
meeting
September 10
,
Wednesday
Aaron Phillips (UVa): Representations of general linear and
symmetric
groups
September 15
,
Monday 3:30 --5:30 (joint with Geometry Seminar)
Mikhail Khovanov (UC Davis)
First
half: Link homology. Second half: Homological
algebra and tangle cobordisms
September 17
,
Wednesday
Shun-Jen Cheng (National Taiwan University): A survey of Lie
superalgebras
September 24
,
Wednesday
Bruce Allison (Alberta, Canada): Loop algebras of Lie algebras
October 1, Wednesday (student presentations)
Michial Thompson (UVa): Partitions and q-series
identities,
I
David Taylor (UVa): Partitions
and q-series identities, II
October 10, Friday 3:30
Mark Shimozono (Virginia Tech): The Zelevinsky map and the ratio formula
for
quiver polynomials
October 15, Wednesday
Shun-Jen Cheng (National Taiwan University): Howe duality and
symmetric
function identities
October 22, Wednesday
Brian Parshall (UVa): Tilting modules for beginners
October 31, Friday 3:30
Yuri Berest (Cornell): Quasi-invariants of complex reflection groups
November 5, Wednesday
Pierre-Emmanuel Caprace (Brussels/UVa): Isomorphisms of Kac-Moody groups
November 12, Wednesday (student presentations)
Dominic Braun (UVa): Presentations
of groups acting on simplicial complexes
Bill Kranec (UVa): Finite
subgroups of quaternions
November 14, Friday (student presentations)
Brian Kapp (UVa): Dimension formulas for an irreducible module of the
symmetric
group
Lorena Bociu (UVa): The Robinson-Schensted-Knuth correspondence
November 19, Wednesday
Ping Xu (Penn State): Quantization of dynamical r-matrices
November 21, Friday (student presentations)
Jess Audit (UVa): A
double cover of the symmetric group
Matthew Pons (UVa): On partition theorems of Fine and Dyson
November 26, Wednesday
No
talk (Thanksgiving break)
December 5, Friday, 3:30 (student presentations)
Jill McCarthy: The
Irreducible $k[S_n]$-modules for $k$ an algebraically closed field of
characteristic
$p \geq 0$
Katie Gorder: Miniquaternion Geometry: The Four Projective Planes of
Order
Nine
Mike Dean: Representations
and characters of wreath products
December 15, Monday, 2:30
(student presentations)
Wess Cramer (UVa)
: Complete varieties
Joe Fox
:
Classification of
reductive groups
------------------------------------------------------------
Spring Semester, 2003.
January 22, Wednesday.
Hendrik Van Maldeghem (Univ. of Ghent): On the Moufang condition
for generalized quadrangles
January 31, Friday (NOTE the special day), 2pm.
Bob Griess Jr. (Univ. of Michigan): A new uniqueness proof
for the E_8 lattice
Feb 5, Wednesday.
Charles Dunkl (UVA): Complex reflection groups
Feb 12, Wednesday.
Stuart Margolis (Bar-Ilan University, Israel/UVA):
Automata and semigroup theoretic algorithms for subgroups of free and
related
groups
Feb 21, Friday (NOTE the special day), 2pm.
Eric Sommers (IAS/UMass-Amherst):
On
the
semisimple conjugacy class attached to a nilpotent orbit in a simple
Lie
algebra
Feb 26, Wednesday.
Stuart Margolis (Bar-Ilan University, Israel/UVA):
Automata and semigroup theoretic algorithms for subgroups of free and
related groups II.
March 5, Spring break, no talk.
March 19, Wednesday.
John Faulkner (UVA): Duals of algebras
April 2, Wednesday.
Harold Ward (UVA): The Basics of Algebraic Coding Theory.
April 9, Wednesday.
Harold Ward (UVA): Special Codes.
April 18, Friday (note the special day), 2pm.
Shrawan Kumar (UNC-Chapel Hill): A conjectural
generalization
of n! result to arbitrary groups
April 23, Wednesday.
Olivier Pfister (UVA): Group representation theory
in
physics and quantum computing
April 25, Friday (note the special day), 2pm.
Harold Ward (UVA): Recent Developments in Coding Theory.
April 30, Wednesday.
Harold Ward (UVA): More recent Developments in
Coding
Theory
------------------------------------------------------------
Fall Semester, 2002.
September 18.
Harold Ward (UVA): Designs and Codes.
September 25.
Harold Ward (UVA): Designs and Codes, II
October 2.
Peter Abramenko (UVA): Some rings with SL_2(R) unequal to E_2(R)
I: A survey
October 9.
No talk is scheduled (due to the department faculty meeting)
October 16.
Weiqiang Wang (UVA): The class algebra of the symmetric group
and
its variants
October 23.
Kevin McCrimmon (UVA): Was sind und was sollen die Jordan
Algebren.
November 1, Friday (NOTE the special day), 2pm.
Boris Tsygan (Northwestern): Index theory, operads, and
deformations
November 6.
Weiqiang Wang (UVA): The symmetric groups and vertex operators
November 13. [Tea 3:30--4:00]
Sylvia Weigand (NSF and University of Nebraska): Prime
ideals
in Noetherian rings
November 15, Friday (NOTE the special day), 2pm.
Milen Yakimov (Cornell): Belavin-Drinfeld Poisson structures on
simple
Lie groups
November 20.
Peter Abramenko (UVA):
Some rings with SL_2(R) unequal to E_2(R) II: Applications of
Bass-Serre
theory
December 4, Wednesday.
Chirashree Bhattacharya (UVA): Representations of Aut(F_2) on
relation
modules