Speaker: Colin Ingalls, University of New Brunswick, Fredericton
Time/Date: Thursday, March 31, 2016, 1:00 p.m.
Room: HH-3017
Title: Birational Classification of Noncommutative Varieties that are Finite over their Centres

Abstract:
We introduce the problem of birational classification for usual commutative varieties as the algebraic problem of classifying fields of finite transcendence degree over the complex numbers using algebraic geometry. In particular a fintely generated field extension of the complex numbers of transcendence degree one corresponds to a unique compact smooth Riemann surface. We extend this problem to the classification of division algebras which are finite dimensional over their centres. The case of curves is a consequence of Tsen's Theorem, and surfaces were studied by Chan and myself in 2005, Recently, we solved this problem in all dimensions and the solution has applications to birational geometry beyond the original problem. This recent work is joint with Daniel Chan, Kenneth Chan, Louis de Thanhoffer de Volcsey, Kelly Jabbusch, Sandor Kovacs, Rajesh Kulkarni, Boris Lerner and Basil Nanayakkara.

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Speaker: István Heckenberger, University of Marburg
Time/Date: Friday, March 18, 2016, 2:00 pm
Room: HH-3017
Title: Fomin-Kirillov algebras

Abstract:
Fomin-Kirillov algebras are certain quadratic algebras graded by the symmetric groups. They and related algebras have been introduced by Fomin and Kirillov in 1998. A particular subalgebra of the Fomin-Kirillov algebra is suitable for calculations with Schubert polynomials. Fomin-Kirillov algebras also appear naturally in the theory of pointed Hopf algebras. Nevertheless almost nothing is known about the structure of these algebras, not even their dimension or a linear basis. In the talk I will present some known facts and some new ideas.

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Speaker: Victor Kac, Massachusetts Institute of Technology
Time/Date: Tuesday, August 26, 2014, 3 p.m.
Room: SN-2109
Title: Ramanujan mock theta function and representations of infinite-dimensional Lie superalgebra

Distinguished Colloquium

Abstract:
 In his last letter to Hardy in 1920, Ramanujan listed 17 functions, which he called "mock theta functions" since they behave like theta functions but have no modular invariance properties of theta functions. Since then there have been substantial progress in understanding of mock theta functions.
About 10 years ago, Zwegers introduced non-holomorphic corrections, which made these functions modular. In the recent work with Wakimoto, we linked mock theta functions to representation theory of affine Lie superalgebras. This in turn sheds new light on the theory of mock theta functions.

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Speaker: Yuanlin Li, Brock University 
Time/Date: November 28, 2012, 1 p.m.
Room: HH-3017
Title: Zero-divisor Graphs of Group Rings (Joint with Dr. Farid Aliniaeifard, Brock University)

Abstract available here.

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Speaker: Nicolas Andruskiewitsch (University of Cordoba, Argentina)
Time/Date: July 25, 2012, 1 p.m.
Room: HH-3017
Title: The classification problem for finite-dimensional Hopf algebras

Departmental Colloquium

Abstract:
Hopf algebras were introduced by Cartier in the middle of the 1950' as an axiomatization of the work of Dieudonne on algebras of distributions on algebraic groups in positive characteristic. Independently, an analogous notion appeared in the works of Hopf and A. Borel. A milestone in the development of the theory was the discovery by Drinfeld and Jimbo of quantum groups, which related Hopf algebras to other areas of mathematics. In the first part of the talk, I will introduce Hopf algebras from scratch, give some basic examples and briefly sketch some aspects of their history. In the second part, I will discuss the classification program of finite-dimensional complex Hopf algebras. An overview of the current state of the art will be given.

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Speaker: Eduardo Martinez-Pedroza, Memorial University of Newfoundland
Time/Date: February 1, 2012
Title: Residual finiteness, subgroup separability and non-positively curved groups

Abstract:
In this talk the notions of residual finiteness and subgroup separability were discussed in connection with non-positively curved groups. Research on non-positively curved groups is motivated by the study of lattices in real rank one semi-simple Lie groups and manifold topology. Open questions, motivation, and some of my work in the area were discussed.

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November 16, 2011

Sara Faridi (Dalhousie University) "Combinatorics and Commutative Algebra"

Abstract:
This talk is about using graphs and hypergraphs to study questions in commutative algebra. I discussed how problems in commutative algebra had led to the description of combinatorial structures that seemed to fit surprisingly well in the existed combinatorics literature. I also discussed open questions, and what the answers "should" look like.

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January 12, 2011

Hugh Thomas (University of New Brunswick) "Garside structures for braid groups"

Distingushed Colloquium 

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October 6, 2010

Gerhard Pfister (University of Kaiserslautern, Germany) “SINGULAR and Applications”

Distingushed Colloquium 

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April 1, 2010

Donald S. Passman "Maximal Filtrations of Semisimple Rings and Lie Algebras"

Distingushed Colloquium 

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March 26, 2010

Mitja Mastnak (Saint Mary's University) "Hopf Algebras in Combinatorics"

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January 27, 2010

Mikhail Kotchetov (Memorial University of Newfoundland) "Group gradings on simple Lie algebras"

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May 29, 2009

Cesar Polcino Milies (University of Sao Paulo) "Group Algebras in Coding Theory"

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May 21, 2008

Nicolas Andruskiewitsch (University of Cordoba, Argentina) "Hopf Algebras: from Hyperalgebras to Quantum Groups"

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November 2, 2007

John Irving (St. Marys University) "Counting Factorizations of Permutations into Star Transpositions"

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August 20, 2007

Alexandre Zalesski (University of East Anglia, UK) "Hurwitz groups: The classification problem"

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May 23, 2007

Alexander Premet (Memorial University of Newfoundland) "Classification of the finite-dimensional simple Lie algebras of characteristic

Distinguished Colloquium

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February 22, 2007

Roman Smirnov (Dalhousie University) "Classical Invariant Theory Revisited"

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November 30, 2006

Margaret Beattie (Mount Allison University) "Coalgebras and Bilinear Forms"

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November 1, 2006

Vladislav Kharchenko (UNAM, National University of Mexico) "Lie algebras and their generalizations" 

Departmental Colloquium

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October 4, 2006

Amitai Regev "On asymptotic growth in PI algebras"

Distinguished Colloquium