26 Jan: Diane Maclagan Stanford "Toric Hilbert schemes" (talk at 4:30 PM) 28 Jan: Greg Smith Columbia "Orbifold Cohomology of Toric Stacks" (talk at 11:30 AM) 30 Jan: Anna Lachowska MIT "TBA" (talk at 1:10 PM) 6 Feb: Chuck Weibel Rutgers "A survey of non-Desarguesian planes" 13 Feb: Kia Dalili Rutgers "The HomAB Problem" 20 Feb: Vladimir Retakh Rutgers "An Introduction to A-infinity Algebras" 27 Feb: Vladimir Retakh Rutgers "An Introduction to A-infinity Algebras II" 5 Mar: Remi Kuku IAS "A complete formulation of the Baum-Connes Conjecture for the action of discrete quantum groups" 12 Mar: Amnon Yekutieli Ben Gurion Univ. "On Deformation Quantization in Algebraic Geometry" 19 Mar: no seminar ------------- Spring Break ------------- 26 Mar: Alexander Retakh MIT "Conformal algebras and their representations" 2 Apr: Aaron Lauve Rutgers "Capture the flag: towards a universal noncommutative flag variety" 9 Apr* Stefano Capparelli Univ. Rome "The affine algebra A22 and combinatorial identities" 16 Apr: Uwe Nagel U.Kentucky "Extremal simplicial polytopes" 16 Apr(C) Dale Cutkosky U. Missouri Colloquium Talk at 4:30 PM 23 Apr* Paul Rabinowitz Wisconsin *** D'Atri Lecture at 1:10 PM *** 23 Apr: Li Guo Rutgers-Newark "Dendriform algebras and linear operators" 30 Apr: Earl Taft Rutgers "There exists a one-sided quantum group" 7 May Student Body Left Rutgers ---- Final Exam Grading Marathon -------- Classes begin January 20, 2004 Spring Break is March 13-21, 2004 Regular classes end Monday May 3. Final Exams are May 6-12, 2004. Math Group Final Exam time is Thursday May 6 (4-7PM) RUTGERS ALGEBRA SEMINAR - Spring 2004
5 Sept George Willis U. South Wales "scale functions on totally disconnected groups" 5 Sept Colonel Henry Rutgers -------- Department Reception ---------------- 8 Sept Various people -------- Gelfand 90th Birthday Celebration -------------- 12 Sept Edwin Beggs U.Wales-Swansea, UK "Constructing tensor categories from from finite groups" 19 Sept Charlie Sims Rutgers "Algorithmic Questions in Rings of Rational Matrices?" 26 Sept David Radnell Michigan Thesis Defense: "Schiffer Variation in Teichmüller space, determinant line bundles and modular functors" 3 Oct* Liang Kong Rutgers "Open-string vertex algebras" 10 Oct C. Musili U.Hyderabad, India "The Development of Standard Monomial Theory" 17 Oct Roy Joshua Inst. Adv. Study "The Motivic DGA" 24 Oct Bodo Pareigis Univ. Munich "Modules, Comodules, Entwinings and Braidings" 31 Oct* Benjamin Doyon Rutgers "From vertex operator algebras to the Bernoulli numbers" 7 Nov* Geoffrey Buhl Rutgers "Complete reducibility and C_n-cofiniteness of vertex operator algebras" 14 Nov no RU seminar ------ Borel Memorial at IAS ----------- 21 Nov* Lin Zhang Rutgers "A vertex operator algebra approach to the construction of a tensor category of Kazhdan-Lusztig" 28 Nov: Tom Turkey ----------Thanksgiving Break------------ 5 Dec* Victor Ostrik IAS "Finite extensions of vertex algebras" 12 Dec* Matt Szczesny U. Penn. "Orbifolding the chiral de Rham complex" Semester begins Tuesday September 2, 2003. Lewis Lectures are the week of October 3rd. Regular classes end Wednesday, December 10. Final Exams are Dec. 15-22. Math Group Exam time is Monday Dec.15 (4-7PM) RUTGERS ALGEBRA SEMINAR - Fall 2003 (in room H425)
28 Jan* Masahiko Miyamoto Japan "Interlocked modules and pseudo-trace functions" 31 Jan: no seminar ------------- Jean Taylor Symposium ------------- 5 Feb: Angela Gibney Michigan "Some open questions about the geometry of the moduli space of curves" 21 Feb* Kiyokazu Nagatomo Japan "Conformal field theory over the projective line" 28 Feb: Jooyoun Hong Rutgers "Normality of Rees algebras for conormal modules" 7 Mar*: Yucai Su Shanghai/Harvard "Lie algebras associated with derivation-simple algebras" 14 Mar* Chengming Bai Nankai&Rutgers "Novikov algebras and vertex (operator) algebras" 21 Mar: no seminar ------------- Spring Break ------------- 28 Mar*: David Radnell Rutgers "Schiffer Variation in Teichmüller Space and Determinant Line Bundles" 3 Apr: Claudio Pedrini U.Genova "Finite dimensional motives" Thursday 3PM - Note change in day! 4 Apr# Hy Bass & Deborah Ball Michigan "Preparing teachers for the mathematical work of teaching" 11 Apr*: Lin Zhang Rutgers "Tensor category theory for modules for a vertex operator algebra -- introduction and generalization" 18 Apr: Constantin Teleman Cambridge U. "Twisted K theory from the Dirac spectral flow" 25 Apr* Michael Roitman Michigan "Affinization of commutative algebras" 2 May: Frederick Gardiner CUNY "The pure mapping class group of a Cantor set" At 1:30 PM - Note change in time! 9 May: Carlo Mazza Rutgers "Schur's Finiteness conditions in tensor categories" At 3:30 PM in H425 - Note change in time and room! Regular classes end Monday May 5. Final Exams are May 8-14, 2003. Math Group Final Exam time is Thursday May 8 (4-7PM) RUTGERS ALGEBRA SEMINAR - Spring 2003
6 Sep: no seminar Rosh Hoshanah 13 Sep: no seminar Department Reception 20 Sep* YZ Huang Rutgers "Differential equations, duality and modular invariance" 27 Sep* Matthias Gaberdiel Kings College "Conformal field theory and vertex operator algebras" 4 Oct: no seminar 11 Oct: Ravi Rao TATA "Raga Bhimpalasi: The Vaserstein-Suslin Jugalbandhi" 11 Oct(C) Igor Kriz Michigan Colloquium Talk "Conformal field theory and elliptic cohomology" at 4:30 PM 18 Oct: Richard Stanley MIT Jacqueline Lewis Lecture at 4:30PM 18 Oct*: Earl Taft Rutgers "Is there a one-sided quantum group?" 25 Oct:Christian Kassel CNRS-Univ. Louis Pasteur, Strasbourg "Explicit norm one elements for ring actions of finite abelian groups" 25 Oct(C) C. Kassel ""(Strasbourg) Colloquium Talk "Recent developments on Artin's braid groups" at 4:30PM 1 Nov* Benjamin Doyon RU Physics "Twisted vertex operator algebra modules and Bernoulli polynomials" 8 Nov: Charles Weibel RU "The work of Vladimir Voevodsky" 15 Nov* Takashi Kimura IAS/Boston U. "Integrable systems and topology" 22 Nov: Julia Pevtsova IAS "Support Varieties for Finite Group Schemes" 29 Nov: Tom Turkey ----------Thanksgiving Break------------ 6 Dec: Anya Lachowska MIT "Modular group action in the center of the small quantum group" RUTGERS ALGEBRA SEMINAR - Fall 2002
25 Jan: no seminar Job Interview Talks 1 Feb: no seminar Job Interview Talks 8 Feb* Liz Jurisich College of Charleston "The monster Lie algebra, Moonshine and generalized Kac-Moody algebras" 15 Feb:j Will Toler RU Physics "Low dimensional topology and gauge theory" 22 Feb# Laura Alcock RU Math/Ed "The first course in real analysis in England: figuring out the conceptions students form" 1 Mar: ----- -- CANCELLED 8 Mar*j Benjamin Doyon RU Physics "Vertex Operator Algebras and the Zeta function" 15 Mar*j Gordon Ritter Harvard "Montonen-Olive Duality in Yang-Mills Theory" 22 Mar: no seminar ------------- Spring Break ------------- 29 Mar* Sergei Lukyanov RU Physics "Once again about Bethe Ansatz" 5 Apr:j Benjamin Doyon RU Physics "Fractional Derivatives" 12 Apr: Lisa Carbone RU "Lattice subgroups of Kac-Moody groups over finite fields" 19 Apr: Agata Smoktunowicz Yale/Warsaw(PAS) "A simple nil ring exists" 26 Apr: Earl Taft RU "Recursive Sequences and Combinatorial Identities" 3 May* Yi-Zhi Huang RU "Differential equations and intertwining operators" 10 May: Calculus Profs Rutgers "Grading of Final Exams" Regular classes end Monday, May 6. Final Exams end Wednesday, May 15. Math Group Exam time is Thursday May 9th (4-7PM). RUTGERS ALGEBRA SEMINAR - Spring 2002
07 Sep: Rutgers Math Department Reception (4PM) 14 Sep* Sasha Kirillov SUNY Stony Brook "On a q-analog of the McKay correspondence" 21 Sep: Ngo Viet Trung Inst.Math.Hanoi "Hilbert functions of non-standard bigraded algebras" 5 Oct: Ed Letzter Temple "Effective Representation Theory of Finitely Presented Algebras" 12 Oct* Yi-Zhi Huang Rutgers "Vertex operator algebras and conformal field theories" 19 Oct: V. Retakh Rutgers "Algebra and combinatorics of pseudo-roots of noncommutative polynomials and noncommutative differential polynomials" 26 Oct*: Yan Soibelman Kansas State U. "Elliptic curves and quantum tori" 2 Nov* Yi-Zhi Huang Rutgers "Vertex operator algebras and conformal field theories II" 9 Nov* Deepak Parashar MPI Leipzig "Some biparametric examples of Quantum Groups" 16 Nov* Yi-Zhi Huang Rutgers "Vertex operator algebras and conformal field theories III" 23 Nov: Tom Turkey ----------Thanksgiving Break------------ 30 Nov* Hai-Sheng Li Rutgers Camden "Certain noncommutative analogues of vertex algebras" 7 Dec: Chuck Weibel Rutgers "Congruence subgroups of SL2(Z[1/n]), after Serre" 14 Dec: regular classes end Wednesday, December 12. Final Exams are Dec. 15-22. Math Group Exam time is Monday Dec.17 (4-7PM) RUTGERS ALGEBRA SEMINAR - Fall 2001
26 Jan: Alexei Borodin U.Penn ------- Job Candidate Interview ------- 2 Feb: Chuck Weibel Rutgers "POSTPONED TO March 30" 9 Feb: Dave Bayer Columbia U. "Toric Syzygies and Graph Colorings" 16 Feb: Igor Kriz U.Michigan "A geometric approach to elliptic cohomology" 23 Feb* Yi-Zhi Huang Rutgers "Conformal-field-theoretic analogues of codes and lattices" 2 Mar: Carl Futia Southgate Capital Advisors "Bialgebras of Recursive Sequences and Combinatorial Identities" 9 Mar* Haisheng Li Rutgers Camden "Regular representations for vertex operator algebras" 16 Mar: no seminar ------------- Spring Break ------------- 23 Mar* Yvan Saint-Aubin U.Montreal+IAS "Boundary behavior of the critical 2d Ising model" 30 Mar: Chuck Weibel Rutgers "Functors with transfer (on rings)" 6 Apr*: Richard Ng Towson U "The twisted quantum doubles of finite groups" 13 Apr* Charles Doran Columbia "Variation of the mirror map and algebra-geometric isomonodromic deformations" 20 Apr*: Lev Borisov Columbia "Elliptic genera of singular algebraic varieties" 27 Apr: Diane Maclagan IAS "Supernormal vector configurations, Groebner fans, and the toric Hilbert scheme 4 May: Calculus Profs Rutgers "Grading of Final Exams" Regular classes end Monday, April 30. Final Exams end Wednesday, May 9. Math Group Exam time is Thursday May 3rd (4-7PM) RUTGERS ALGEBRA SEMINAR - Spring 2001
8 Sep: Amelia Taylor Rutgers "The inverse Gröbner basis problem in codimension two" 15 Sep* Mike Douglas RU Physics "D-branes" 22 Sep: Chuck Weibel Rutgers "Topological vs. algebraic $K$-theory for complex varieties" 29 Sep: no seminar ------------- Rosh Hoshanna ------------ 6 Oct: Daya-Nand Verma TATA Inst. "Progress Report on the Jacobian Conjecture" 13 Oct: no seminar 20 Oct* Constantin Teleman U.Texas "The Verlinde algebra and twisted K-theory" 27 Oct: Chuck Weibel Rutgers "Homotopy Ends and Thomason Model Categories" 3 Nov* Mirko Primc U.Zagreb "Annihilating fields of standard modules of sl_2~ and combinatorial identities" 10 Nov: Suemi Rodriguez-Romo UNAM Mexico "Quantum Group Actions on Clifford Algebras" 17 Nov: Craig Huneke U.of Kansas "Growth of Symbolic Powers in Regular Local Rings" 24 Nov: Tom Turkey ----------Thanksgiving Break------------ 1 Dec# Nina Fefferman and Matt Young Rutgers VIGRE presentations on p-adic numbers 8 Dec* Mike Douglas? RU Physics "D-branes, instantons and orbifolds" RUTGERS ALGEBRA SEMINAR - Fall 2000
4 Feb: Martin Sombra IAS+LaPlata "Division formulas and the arithmetic Nullstellensatz" 11 Feb: no seminar 18 Feb: Claudio Pedrini IAS+Genoa "K-theory of algebraic varieties: a Survey" 25 Feb: M.R.Kantorovitz IAS "Andre-Quillen homology from a calculus viewpoint" (with Hochschild homology and algebraic K-theory for dessert) 3 Mar: S. Hildebrandt Bonn *** D'Atri Lecture *** (2-dim. Variational Problems) 10 Mar: D. Christensen IAS "Brown representability in derived categories" 17 Mar: --- ---- ------- Spring Break ----------- 24 Mar* Haisheng Li RU-Camden "Certain extended vertex operator algebras" 31 Mar* Christoph Schweigert Paris "Conformal boundary conditions and three-dimensional topological field theory" 7 Apr: no seminar 14 Apr* Christian Schubert LAPTH France "Multiple Zeta Value Identities from Feynman Diagrams" 21 Apr: no seminar 28 Apr* Tony Milas Rutgers "Structure of fusion rings associated to Virasoro vertex operator algebras" 3 May* (Wednesday) Tony Milas Rutgers "Differential operators and correlation functions" RUTGERS ALGEBRA SEMINAR - Winter 2000
24 Sep: V. Retakh Rutgers "Noncommutative rational functions+Farber's invariants of boundary links" 1 Oct: Antun Milas* Rutgers "Intertwining operator superalgebras for N=1 minimal models" 8 Oct: Fedor Bogomolov NY Univ "Fundamental Groups of Projective Varieties" 15 Oct: Earl Taft Rutgers "Sequences satisfying a polynomial recurrence" 22 Oct: Yuji Shimizu* Kyoto U "Momentum mappings and conformal fields" 29 Oct: Leon Seitelman U.Conn. SPECIAL VIGRE LECTURE "What's a mathematician like you doing in a place like that" 5 Nov: Keith Pardue IDA/Princeton "Generic Polynomials" 12 Nov: *Haisheng Li Rutgers (Camden) "The Diamond lemma for algebras (following Bergman)" 19 Nov: Yuri Tschinkel U.Illinois "Equivariant compactifications of G_a^n" 26 Nov: Tom Turkey ------Thanksgiving Break-------- 3 Dec: Borisov* Columbia "Vertex algebras and mirror symmetry" 10 Dec: Chongying Dong UC Santa Cruz "Holomorphic orbifold theory, quantum doubles and dual pairs" RUTGERS ALGEBRA SEMINAR - Fall 1999
22 Jan: P. Balmer Rutgers "The derived Witt group of a ring" 29 Jan: W. Vasconcelos Rutgers "The intertwining algebra" 5 Feb: Thomas Geisser U.Tokyo "TBA" 12 Feb:Dennis Gaitsgory Harvard/IAS "On a VOA of differential operators on a loop group" 19 Feb: Mark Walker Nebraska "The total Chern class map" 26 Feb: Michael Roitman Yale "Universal constructions in conformal and vertex algebras" 5 March: E. Friedlander Northwestern "Re-interpreting the Bloch-Lictenbaum spectral sequence" 12 March: R. Schoen D'Atri Lecture instead of seminar 19 March: Vernal Equinox ------Spring Break March 14-21---- 26 March: Yuji Shimizu Kyoto and Rutgers "Conformal blocks and KZB equations" 2 April: Roger Rabbit Toontown no seminar (Passover/Easter) 9 April: 16 April: Marco Schlichting RU and U. Paris "The negative K-theory of an exact category" 23 April: Chuck Weibel Rutgers "Projective modules over normal surfaces" 30 April: Percy Deift Courant Institute (Colloquium talk) 7 May: Yuji Shimizu Kyoto and Rutgers "Geometric structures underlying some conformal field theories" RUTGERS ALGEBRA SEMINAR - Spring 1999
18 Sep: Lowell Abrams Rutgers "Modules, comudules and cotensor products over Frobenius algebras" 25 Sep: Bogdan Ion Princeton "Maschke's theorem revisited" 2 Oct: Haisheng Li(*) Rutgers Camden "An infinite-dimensional analogue of Burnside's theorem" 9 Oct: Aron Simis Univ.F.Pernambuco (Recife, Brazil) "Geometric Aspects of Rees Algebras" 16 Oct: A. Beilinson Univ. Chicago Colloquium in honor of Gelfand 23 Oct: Michael Finkelberg(*) IAS/Independent Moscow Univ. "An integrable system on the space of based maps from P^1 to a flag variety" 30 Oct: Yi-Zhi Huang(*) Rutgers "Semi-infinite forms and topological vertex operator algebras" 6 Nov: Alfons Ooms Limburgs Univ, Belgium "On the Gelfand-Kirillov conjecture" 13 Nov: A. Kirillov, Jr.(*) IAS "On the Lego-Teichmuller game" 20 Nov: M.F. Yousif Ohio State-Lima "On three conjectures on quasi-Frobenius Rings" 27 Nov: Tom Turkey ------Thanksgiving Break-------- 4 Dec: C. Lenart Max Planck (Bonn) "" 11 Dec: S. Majid Cambridge Univ. "braided groups and the inductive construction of U_q(g)" RUTGERS ALGEBRA SEMINAR - Fall 1998
30 Jan: C. Weibel Rutgers "local homology vs. cohomology (after Greenlees-May)" 6 Feb: Brian Parshall U. of Virginia "The cohomology and representation theory of reductive groups in non-describing characteristics" 13 Feb: M. Khovanov(*) Yale and IAS "Lifting the Jones polynomial of knots to invariants of surfaces in 4-space" 20 Feb: Ming-Sun Li Rowan Univ. "Spectral matrices associated to an algebra" 27 Feb: Yi-Zhi Huang(*) Rutgers "Analytic aspects of Intertwining Operators" 6 Mar: Boris Khesin(*) IAS+U.Toronto "Geometric complexification of affine algebras and flat connections on surfaces" 13 Mar: no algebra seminar 20 Mar: Vernal Equinox ------Spring Break-------- 27 Mar: N. Inassaridze Razmadze Inst. "Non-abelian homology of groups" 3 Apr: Jim Stasheff UNCarolina "Physically inspired homological algebra" 10 Apr: Movshev(*) ... QUANTUM MATH SEMINAR 17 Apr: S. Sahi Rutgers "A new character formula for compact Lie groups" 24 Apr: Stefan Schmidt Berkeley "Projective Geometry of Modules" 1 May: Toma Albu U.Wisc.-Milwaukee "GLOBAL KRULL DIMENSION AND GLOBAL DUAL KRULL DIMENSION OF RINGS" Spring 1998 ALGEBRA SEMINAR
19 Sep: Bill Kantor U. Oregon Colloquium: "Black box classical groups" 26 Sep: Lowell Abrams Rutgers "2-dimensional TQFT's and Frobenius Algebras" 3 Oct: --- ------ Rosh Hoshanna ----- 10 Oct: Tor Gunston Rutgers "Degree functions and linear resolutions" 31 Oct: Chuck Weibel Rutgers "introducing Motives" 7 Nov: --- Columbia Univ. Bass Conference 14 Nov: Stefan Catoiu Temple Univ. "IDEALS OF THE ENVELOPING ALGEBRA U(sl_2)" 21 Nov: M. Kontsevich IHES "Deformation, Quantization and Beyond" 28 Nov: Tom Turkey ------Thanksgiving Break-------- 5 Dec: M. Kontsevich IHES "Deformation, Quantization and Beyond" 12 Dec: C. Pedrini U. Genova "K-Theory and Bloch's Conjecture for complex surfaces" Fall 1997 ALGEBRA SEMINAR
31 Jan: Luisa Doering Rutgers "Generalized Hilbert functions" 7 Feb: postponed 14 Feb: Miguel Ferrero Porto Alegre,Brazil "Closed and prime submodules of centered bimodules and applications to ring extensions" 21 Feb: Richard Ng Rutgers "Freeness of Hopf algebras over subalgebras" 28 Feb: Siddartha Sahi Rutgers "Introduction to Macdonald polynomials" 7 Mar: Barbara Osofsky Rutgers "Projective dimension for commutative von Neumann regular rings and a new lattice invariant" 14 Mar: Chuck Weibel Rutgers "K-theory and zeta functions on number fields" 21 Mar: ------------ Spring Break ------------ 28 Mar: Carl Faith Rutgers "Rings with ACCs on annihilators" 4 Apr: Joe Brennan N.Dakota "The Ends of Ideals" 11 Apr: Jan Soibelman Kansas State "Meromorphic tensor categories and quantum affine algebras" 18 Apr: Chuck Weibel Rutgers "Tor without identity (after Quillen)" 25 Apr: Wolmer Vasconcelos Rutgers "Integral closure" 2 May: Luca Mauri Rutgers "2 torsors, TBA" RUTGERS ALGEBRA SEMINAR - Spring 1997
20 Sep: C. Weibel Rutgers "the 2-torsion in the K-theory of Z" 27 Sep: Tor Gunston Rutgers "Cohomological dimension of graded modules" 4 Oct: B. Ulrich MichState "Divisor class groups and Linkage" 11 Oct: -- IAS Langlands Fest 18 Oct: Bob Guralnick USC "Finite Orbit Modules and Double Cosets for Algebraic Groups" 25 Oct: Richard Weiss Tufts "Moufang polygons" 1 Nov: Georgia Benkart Wisconsin "Lie Algebras Graded by Finite Root Systems" 8 Nov: Richard Ng Rutgers "On the projectivity of module coalgebras" 15 Nov: -- no seminar 22 Nov: Bill Keigher RU-Newark "The ring of Hurwitz series" 29 Nov: Tom Turkey Thanksgiving (no seminar) 6 Dec: Leon Pritchard RU-Newark "Hurwitz series Formal Functions" 13 Dec: Reading Period after classes RUTGERS ALGEBRA SEMINAR - Fall 1996
26 Jan: A.Corso Rutgers "generic gaussian ideals" 2 Feb: no seminar 9 Feb: E. Taft Rutgers "Quantum Convolution" 16 Feb: Frosty S. Weather "Snow storm--talks rescheduled" 23 Feb: B. Leasher Rutgers "Geometric Aspects of Steinberg Groups for Jordan Pairs" 1 Mar: L. Mauri Rutgers "Low-dimensional Descent theory" 8 Mar: K.Consani IAS "Double complexes and local Euler factors on algebraic degeneration" 15 Mar: ------------ Spring Break ------------ 22 Mar: YZ Huang Rutgers "On algebraic D-modules and vertex algebras" 29 Mar: Doering&Gunston Rutgers "Algebras Arising from Bipartite Planar Graphs" 5 Apr: Consuelo Martinez Yale "Power subgroups of profinite groups" 12 Apr: M. Singer NC State "Galois theory for difference equations" 19 Apr: C. Weibel Rutgers "Popescu Desingularization (after Swan)" 26 Apr: R. Hoobler CCNY "Merkuriev-Suslin Theorem for arbitrary semi-local rings" 14 May: K. Mimachi Kyushu U. "Quantum Knizhink-Zamolodchikov equation and eigenvalue problem of Macdonald equations" ALGEBRA SEMINAR - Spring 1996
27 Jan Alberto Corso Rutgers "Links of irreducible varieties" 3 Feb Chuck Weibel Rutgers "Operads for the Working Mathematician" 10 Feb Maria Vaz Pinto Rutgers "Hilbert Functions and Sally Modules" 17 Feb Yi-Zhi Huang Rutgers "Vertex Operator Algebras for Lay Algebraists" 24 Feb O. Matthieu "On the modular representations of the symmetric group" 3 Mar Claudio Pedrini Genova "The Chow group of singular complex surfaces" 10 Mar B.Sturmfels-Berkly A normal form algorithm for modules over k[x,y]/(xy) 18 Mar ------------ Spring Break ------------ 24 Mar Francesco Brenti IAS "Twisted incidence algebras and Kazhdan-Lusztig-Stanley functions" 31 Mar Myles Tierney Rutgers "Simplicial sheaves" 7 April Wolmer Vasconcelos "A Lemma of Gauss" 14 April Peter Cottontail "Easter's on its way! (Passover too!)" 21 April Susan Morey "Symbolic Powers, Serre Conditions and CM Rees algebras" 28 April K.P. Shum Hong Kong/Maryland "Regular semigroups and generalizations" 5 May ----------- Spring Exam period ----------------- Algebra Seminar, Winter 1995
First meeting was on a Thursday, at 4:30 PM: 28 Sep: M.Gerstenhaber Univ. Pennsylvania "Symplectic structures on max. parabolic subgps. of SL_n and boundary solutions of the classical Yang-Baxter eqn." All other seminar meetings were on Fridays, at 2:50-4PM in H705. 29 Sept:W. Vasconcelos Rutgers "Gauss Lemma" 6 Oct: I. Gelfand Rutgers "Noncommutative symmetric functions" 13 Oct: Joan Elias Barcelona"On the classification of curve singularities" 20 Oct: B. Osofsky Rutgers "Connections between foundations and Algebra" 27 Oct: O. Stoyanov Rutgers "Quantum Unipotent Groups" 3 Nov: I. Gelfand Rutgers "Noncommutative Grassmannians" 10 Nov: M. Tretkoff Stevens "Rohrlich's formula for hypersurface periods" 17 Nov: C. Weibel Rutgers "Tinker Toys and graded modules" 24 Nov: Tom Turkey Thanksgiving Break 1 Dec: Siu-Hung Ng Rutgers "Lie bialgebra structures on the Witt algebra" 8 Dec: E. Zelmanov Yale "On narrow groups and Lie algebras" 15 Dec -- Classes ended on Wed. 13 December ALGEBRA SEMINAR - Fall 1995
Orbifold Cohomology of Toric Stacks
(Greg Smith, Jan 28, 2004):
On Deformation Quantization in Algebraic Geometry
(Amnon Yekutieli, March 12, 2004):
Conformal algebras and their representations
(Alexander Retakh, March 26, 2004):
In this talk, however, I will present conformal algebras as a
self-contained theory and will mostly concentrate on their
representations, in particular, on the conformal analogs of matrix
algebras. These objects are related to certain subalgebras of the
Weyl algebra and the algebra gl{\infty}.
Capture the flag: towards a universal noncommutative flag variety
(Aaron Lauve, April 2, 2004):
The affine algebra A22 and combinatorial identities
(Stefano Capparelli, April 9, 2004):
Extremal simplicial polytopes (Uwe Nagel, April 16, 2004):
Dendriform algebras and linear operators
(Li Guo, April 23, 2004):
There exists a one-sided quantum group
(Earl Taft, April 30, 2004):
If we apply a double construction to this, we arrive at a braided
category and a braided Hopf algebra. It turns out that this is a
ribbon category, and (at least sometimes) a monoidal category.
Open-string vertex algebras
(Liang Kong, Oct. 3, 2003):
The Development of Standard Monomial Theory
(C. Musili, Oct. 10, 2003):
Let G be a semi-simple, connected and simply connected algebraic
group, defined over an algebraically closed field of characteristic
0. Fix a maximal torus T, a Borel subgroup B containing T,
and a maximal parabolic subgroup P containing B. Fix also
the root system of G relative to T, the positive/simple roots relative
to B, etc. Let W = W(G) be the Weyl group of G.
Let V be a fundamental representation of G corresponding to P. The
first main aim of SMT is to construct a
"nice" basis for each of the T-weight subspaces in V, having some
"compatibility" properties with that of the extremal weight spaces and
satisfying some "geometric" properties, etc.
Let M be an irreducible representation of G and express it as a
subquotient of the appropriate tensor product of suitable fundamental
representations of G. The second main aim of SMT is to construct bases
for the weight spaces of M in terms of those constructed for the
fundamental representations.
The Motivic DGA
(Roy Joshua, Oct. 17, 2003):
Modules, Comodules, Entwinings and Braidings
(Bodo Pareigis, Oct. 24, 2003):
Quotients of a smooth variety by a group play an important
role in algebraic geometry. In this talk, I will describe an
interesting collection of quotient spaces (called toric stacks)
defined by combinatorial data. As an application, I will relate the
orbifold cohomology of a toric stack with a resolution of the
underlying singular variety.
We study deformation quantization of Poisson algebraic varieties.
Using the universal deformation formulas of Kontsevich, and an
algebro-geometric approach to the bundle of formal coordinate
systems over a smooth variety X, we prove existence of
deformation quantization of the sheaf of functions OX
(assuming the vanishing of certain cohomologies). Under slightly
stronger assumptions we can classify all such deformations.
Conformal algebras first appeared as an attempt to provide
algebraic formalism for conformal field theory (as part of the
theory of vertex algebras). They are also closely related to
Hamiltonians in the formal calculus of variations.
The standard way to build flag algebras from a set of flags is to use
the determinant to coordinatize the latter (then the former is just the
polynomial algebra in the coordinate functions for these coordinates).
There is a perfectly reasonable notion of noncommutative flags, but
what are we to do about the lack of a determinant in noncommutative
settings?
In this talk I will: (1) use the Gelfand-Retakh quasideterminant to
build a generic noncommutative Grassmannian algebra, (2) specialize
this generic Grassmannian to recover the well-known Taft-Towber quantum
Grassmannian, (3) explain what steps are left before we can build a
generic flag algebra. This talk should be accessible to first and
second year graduate students.
I will give a brief outline of the Lepowsky-Wilson Z-algebra approach
to classical combinatorial identities and the Meurman-Primc proof of
the generalized Rogers-Ramanujan identities. I will next outline the
application of this theory to the construction of the level 3 standard
modules for the affine algebra A22 and the
corresponding combinatorial identities as well as Andrews' combinatorial
proof of these identities. I will discuss some current ideas for a
possible approach to these identities and their generalizations using
intertwining operators. Finally, I will mention the apparent link
between level 5 and 7 standard modules for the affine algebra
A22
and some other Rogers-Ramanujan-type identities of Hirschhorn.
In 1980 Billera-Lee and Stanley characterized the possible numbers of
i-dimensional faces of a simplicial polytope. Its graded Betti
numbers are finer invariants though little is known about them.
However, among the simplicial
polytopes with fixed numbers of faces in every dimension there is
always one with maximal graded Betti numbers. In the talk, this result
will be related to the
more general problem of characterizing the possible Hilbert functions
and graded Betti numbers of graded Gorenstein algebras and key
ideas of its proof will be discussed.
Dendriform algebras refer to a class of algebra structures introduced
by Loday in 1996 with motivation from algebraic K-theory. The field has
expanded quite much during the last couple of years, with connections to
operad theory, math physics, Hopf algebras and combinatorics. A recent
observation is that some basic dendriform algebras are induced by linear
operators, such as Baxter and Nijenhuis operators, and more complicated
such algebras can be decomposed as products in operad theory. We will
discuss these developments.
Bialgebras with a left antipode but no right antipode were
constructed in the 1980's by J.A.Green, W.D.Nichols and E.J.Taft.
Recently, S.Rodriguez-Romo and E.J.Taft tried to construct such
a one-sided Hopf algebra within the framework of quantum groups,
starting with roughly half the defining relations for quantum
GL(2). Asking that the left antipode constructed be an algebra
antimorphism led to some additional relations, but the result
was a new(two-sided) Hopf algebra. Now we start with roughly half
the relations for quantum SL(2) but ask that our left antipode
constructed reverse order only on irreducible monomials in the
generators. The result is a quantum group with a left antipode but no
right antipode.
Constructing tensor categories from from finite groups
(Edwin Beggs, Sept 12, 2003):
First we consider the algebra structure induced on a set of coset
representatives of a subgroup of a finite group. Associated to it is a
non-trivial tensor category, which we construct. There is an algebra
in this category whose representations consist of the entire category.
This is joint work with Y.-Z. Huang.
We introduce notions of open-string vertex algebra, conformal
open-string vertex algebra and variants of these notions. These are
"open-string-theoretic," "noncommutative" generalizations of the notions
of vertex algebra and of conformal vertex algebra. Given an open-string
vertex algebra, we show that there exists a vertex algebra, which we
call the "meromorphic center" inside the original algebra such that the
original algebra yields a module and also an intertwining operator for
the meromorphic center. This result gives us a general method for
constructing open-string vertex algebras. Besides obvious examples
obtained from associative algebras and vertex (super)algebras, we give a
nontrivial example constructed from the minimal model of central charge
c = 1/2 . We also discuss the relationship between the gradingrestricted
conformal open-string vertex algebras and the associative algebras in
braided tensor categories. We also discuss a geometric and operadic
formulation of the notion of such algebra and the relationship between
such algebras and a so-called "Swiss-cheese partial operad.
The main phases of the development of Standard Monomial Theory (SMT)
and some of its applications to Geometry and Commutative Algebra will
be surveyed without assuming anything and, more importantly, without
becoming technical.
We will outline the structure of an E_{\infinity} algebra on the
motivic complex drawing the parallel with the singular complex where
such a structure was provided by Hinich and Schechtman. We will also
consider some applications like the construction of a category of
relative Tate motives for a large class of varieties and the
construction of cohomology operations in motivic cohomology with
finite coefficients. (This is joint work with Peter May.)