Asterisks (*) mark meetings of the QUANTUM MATH SEMINAR, which occasionally replaces the Algebra Seminar. Joint ALGEBRA/QUANTUM meetings are marked ' *: '
A 'j' marks a meeting of the Junior Algebra Seminar; a 'C' marks a related Colloquium Talk at 4:30 PM.
Click here for the algebra seminars in previous semesters

21 Jan:    (first Friday of semester)
28 Jan:
 4 Feb:
11 Feb:
18 Feb:
25 Feb:
 4 Mar:
11 Mar:
18 Mar: no seminar	------------- Spring Break ------------- 
25 Mar:
 1 Apr: Gerhard Michler Univ. Essen and Cornell  (tentative)
 8 Apr:
15 Apr:
22 Apr:
29 Apr:
 6 May: Student Body Left  Rutgers   ---- Final Exam Grading Marathon -------
Classes begin January 18, 2005
Spring Break is March 12-20, 2005
Regular classes end Monday May 2. Final Exams are May 5-11, 2005.

10 Sept Colonel Henry Rutgers -------- Department Reception ----------------
24 Sept*                         Yom Kippur is 9/25
 1 Oct* Liang Kong     Rutgers	 "Conformal field algebras and tensor categories"
 8 Oct:                          MacPherson's 60th Conference
15 Oct: Pavel Etingof  MIT	 "Cherednik and Hecke algebras of orbifolds"
22 Oct* Lin Zhang      RU+Sequent-Capital "When does the commutator formula imply the Jacobi identity in Vertex Operator Algebra theory?"
29 Oct*: A. Ocneanu    Penn State "Modular theory, quantum subgroups and quantum field theory"
 5 Nov: Helmut Hofer   Courant   D'Atri Lecture: Holomorphic Curve Methods (talk at 1:10 PM)
 5 Nov:* Keith Hubbard Notre Dame "Vertex Algebra coalgebras: Their operadic motivation and concrete constructions"
12 Nov: Chuck Weibel   Rutgers   "Homotopy theory for Motives"
19 Nov: Edwin Beggs  Univ. of Wales Swanswa "The Van Est spectral sequences for Hopf algebras"
26 Nov: Tom Turkey   Plymouth Colony ----------Thanksgiving Break------------
10 Dec: Edwin Beggs  Univ. of Wales Swanswa"Quasi-Hopf algebras, twisting and the KZ equation"
17 Dec: Student Body Left  Rutgers   ---- Final Exam Grading Marathon -------

Semester begins Wednesday September 1, 2003.
Regular classes end Monday, December 13. Final Exams are Dec.16-23.
Math Group Exam time is Thursday Dec.16 (4-7PM)


Possible speakers:   (tentatively in Spring 2004)
Myles Tierney	Montreal
Li Guo   RU-Newark

23 Jan:    (first Friday of semester)
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)

Abstracts of seminar talks

Fall 2004

Modular theory, quantum subgroups and quantum field theory (Adrian Ocneanu, Oct. 29, 2004):
We describe the connections between modular invariants, topological quantum doubles and the construction and classification of quantum subgroups. We discuss applications to quantum field theoretical models.

Vertex operator coalgebras: Their operadic motivation and concrete constructions (Liang Kong, Oct. 1, 2004):
Arising from the study of conformal field theory, vertex operator coalgebras model the surface swept out in space-time as a closed string splits into two or more strings. By studying the theory of operads, a structure introduced by May to study iterated loop spaces, the structure of both vertex operator algebras and vertex operator coalgebras may be developed.

This talk will define the notion of operad, show how operads geometrically motivate associative algebras and coassociative coalgebras, and then analogously use operads to motivate vertex operator algebras and vertex operator coalgebras. The talk will conclude with examples of vertex operator coalgebras that are constructed via vertex operator algebras with appropriate bilinear forms.

Homotopy theory for Motives (Charles Weibel, Nov. 12, 2004):
An introduction to the Morel-Voevodsky construction of homotopy theory for algebraic varieties which underlies modern notions of motives. The idea is that a "space" should be a jazzed-up object built up out of varieties using simple constructions like quotients, and that the affine line should play the role of the unit interval.

The Van Est spectral sequences for Hopf algebras
(Edwin Beggs, Nov. 19, 2004):

In classical geometry there have been results about the cohomology of manifolds with Lie group actions, and the relation between the topological cohomology of the group and its Lie algebra cohomology, for about 50 years. I shall give noncommutative analogues of some of these results, in terms of Hopf algebras acting on algebras with differential structure. I shall begin with a brief review of noncommutative differential geometry and de-Rham cohomology.

Quasi-Hoph algebras, twisting and the KZ equation
(Edwin Beggs, Dec. 10, 2004):

In this informal talk I'll give the definition of quasi-Hopf algebras, some examples (and some conjectural examples) of twisting, including the Knizhnik-Zamolodchikov (KZ) equation.

Spring 2004

Orbifold Cohomology of Toric Stacks (Greg Smith, Jan 28, 2004):
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.

On Deformation Quantization in Algebraic Geometry (Amnon Yekutieli, March 12, 2004):
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 O_X (assuming the vanishing of certain cohomologies). Under slightly stronger assumptions we can classify all such deformations.

Conformal algebras and their representations (Alexander Retakh, March 26, 2004):
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.

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 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.

The affine algebra A₂² and combinatorial identities (Stefano Capparelli, April 9, 2004):
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.

Extremal simplicial polytopes (Uwe Nagel, April 16, 2004):
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 and linear operators (Li Guo, April 23, 2004):
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.

There exists a one-sided quantum group (Earl Taft, April 30, 2004):
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.