Algebra Seminar 2002-07

 Fall Semester, 2007

   September 19
   Title: The Steinberg Module and the Steinberg Tensor Product Theorem  
   Speaker: Chris Drupieski (UVa)  

   September 26
   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)

  October 17
  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 21   No talk (Thanksgiving  recess)

  November 28  
Generic extension monoid algebras for cyclic quivers  
  Speaker: Bangming Deng (Beijing Normal University)

  December 5
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

  January 31
   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

September 20
  Speaker: Terrell Hodge (Western Michigan University) 
Title: On Nilpotent Orbits and Desingularizations of Their Closures  

September 27
  No talk

October 4
Ta Khongsap (UVa)
  Title: On Hecke algebras of finite and affine type

October 11
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

November 1
  Speaker: Alexei Oblomkov (Princeton U.)
  Title: Introduction into the Double Affine Hecke algebras

November 8

  Speaker: Shun-Jen Cheng (Academia Sinica, Taipei)
Kostant's homology formula for unitarizable gl_{\infty|\infty}-modules

November 15

  Speaker: Chris Drupieski (UVa)

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
 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)~
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.

  September 7
  Speaker: Dmitriy Sonkin
  Title: Graded diagrams method and the Burnside problem

  September 14
  Speaker: Weiqiang Wang
  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

  September 21
  Speaker: Nick Kuhn (UVA)
  Title: Central extensions of finite groups and cohomology primitives

October 5, No Seminar.

October 12
 Speaker: Kai-Uwe Bux (UVA)
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.

November 2
   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 .

November 23
   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

 February 9, Wednesday, 3:30,
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,
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
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
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

  September 29, Wednesday, No Seminar

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.

  February 25, 3:30 Wednesday,  No seminar due to Faculty meeting

  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

  March 17, 3:30 Wednesday,
  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
   (Note that Leclerc will be giving a colloquium talk on April 8, Thursday, which is the part I of his talks)

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


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