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Yorck Sommerhäuser
Conference Talks



 Quantum 60
 Title: Hochschild cohomology and mapping class groups
 Date: Wednesday, December 12, 2018
 Location: Córdoba, Argentina
 Summary
 AMS Spring Eastern Sectional Meeting: Special session on Hopf algebras, tensor categories, and homological algebra
 Title: Extensions of YetterDrinfel'd Hopf algebras I
 Date: Saturday, April 21, 2018
 Location: Boston, USA
 Summary
 Joint Mathematics Meeting: Special session on structure and representations of Hopf algebras:
a session in honor of Susan Montgomery
 Title: Hochschild cohomology and the modular group
 Date: Thursday, January 11, 2018
 Location: San Diego, USA
 Summary
 Combinatorics of Group Actions and its Applications
 Title: Hopf algebras and associated group actions
 Date: Tuesday, August 29, 2017
 Location: St. John's, Canada
 Summary
 XXII Coloquio Latinoamericano de Álgebra
 Title: Hochschild cohomology and the modular group
 Date: Tuesday, August 8, 2017
 Location: Quito, Ecuador
 Summary
 Joint Mathematics Meeting: Special Session on Hopf Algebras and Their Actions
 Title: YetterDrinfel'd Hopf algebras and their associated algebras
 Date: Wednesday, January 4, 2017
 Location: Atlanta, USA
 Summary
 Groups and Rings  Theory and Applications
 Title: Cores in YetterDrinfel'd Hopf algebras
 Location: Sofia, Bulgaria
 Date: Thursday, July 14, 2016
 Summary
 Brauer Groups, Hopf Algebras and Monoidal Categories
 Title: Cores in YetterDrinfel'd Hopf algebras
 Location: Turin, Italy
 Date: Tuesday, May 24, 2016
 Summary
 AMS Fall Central Sectional Meeting: Special session on groups, rings, group rings, and Hopf algebras
 Title: YetterDrinfel'd Hopf algebras and their extensions
 Location: Chicago, USA
 Date: Sunday, October 4, 2015
 Summary
 Algebraic Groups and Lie Algebras
 Title: YetterDrinfel'd Hopf algebras in Lie theory
 Location: Norris Point, Canada
 Date: Friday, August 21, 2015
 Program
 Joint International Meeting between the AMS, the EMS, and the SPM: Special session on representation theory and quantum groups
 Title: Triviality theorems for YetterDrinfel'd Hopf algebras
 Location: Porto, Portugal
 Date: Thursday, June 11, 2015
 Summary
 New Trends in Hopf Algebras and Tensor Categories
 Title: Triviality in YetterDrinfel'd Hopf algebras
 Location: Brussels, Belgium
 Date: Thursday, June 4, 2015
 Summary
 The Southern Regional Algebra Conference at the University of Louisiana at Lafayette
 Title: Triviality theorems for YetterDrinfel'd Hopf algebras
 Location: Lafayette, USA
 Date: Saturday, March 14, 2015
 Summary
 Joint Mathematics Meeting: Special session on Hopf algebras and tensor categories
 Title: A triviality theorem for YetterDrinfel'd Hopf algebras
 Location: San Antonio, USA
 Date: Monday, January 12, 2015
 Summary
 AMS Fall Eastern Sectional Meeting: Special session on Hopf algebras
 Title: A triviality theorem for YetterDrinfel'd Hopf algebras
 Location: Halifax, Canada
 Date: Sunday, October 19, 2014
 Summary
 The Southern Regional Algebra Conference at Auburn UniversityMontgomery
 Title: YetterDrinfel'd Hopf algebras over groups of prime order
 Location: Montgomery, USA
 Date: Saturday, April 26, 2014
 Program
 Joint International Meeting between the AMS and the RMS: Special session on Hopf algebras and quantum groups
 Title: Involutory quasiHopf algebras and ribbon quasiHopf algebras
 Location: Alba Iulia, Romania
 Date: Sunday, June 30, 2013
 Summary
 Canadian Mathematical Society Summer Meeting: Session on Hopf algebras and tensor categories
 Title: Semilinear actions of general linear groups on character rings of Hopf algebras
 Location: Halifax, Canada
 Date: Thursday, June 6, 2013
 Summary
 AMS Spring Eastern Sectional Meeting: Special session on Hopf algebras and their applications
 Title: Semilinear actions of general linear groups on character rings of Hopf algebras
 Location: Boston, USA
 Date: Saturday, April 6, 2013
 Summary
 The Southern Regional Algebra Conference at Southeastern Louisiana University
 Title: YetterDrinfel'd Hopf algebras
 Location: Hammond, USA
 Date: Saturday, March 16, 2013
 Program
 Lie Theory Workshop
 Title: The index of a character
 Location: Los Angeles, USA
 Date: Saturday, May 5, 2012
 Summary
 The Southern Regional Algebra Conference at Clayton State University
 Title: QuasiHopf algebras and Gaussian sums
 Location: Morrow, USA
 Date: Saturday, March 31, 2012
 Summary
 Joint Mathematics Meeting: Special session on tensor categories and representation theory
 Title: Conductors and exponents
 Location: Boston, USA
 Date: Saturday, January 7, 2012
 Summary
 AMS Fall Central Sectional Meeting: Special session on quantum groups and representation theory
 Title: Deformed enveloping algebras
 Location: Lincoln, USA
 Date: Saturday, October 15, 2011
 Summary
 Hopf Algebras and Tensor Categories
 Title: Bilinear forms, EilenbergMacLane cocycles, and the central charge
 Location: Almería, Spain
 Date: Friday, July 8, 2011
 Summary
 Joint Mathematics Meeting: Special session on Hopf algebras and their representations
 Title: The central charge of factorizable Hopf algebras coming from bilinear forms
 Location: New Orleans, USA
 Date: Saturday, January 8, 2011
 Summary
 The Southern Regional Algebra Conference at the University of Louisiana at Lafayette
 Title: Bilinear forms, Hopf algebras, and Drinfel'd elements
 Location: Lafayette, USA
 Date: Sunday, October 17, 2010
 Program
 The Southern Regional Algebra Conference at Auburn UniversityMontgomery
 Title: Hopf algebras and Gaussian sums
 Date: Friday, March 26, 2010
 Location: Montgomery, USA
 Summary:
With the Rmatrix of a semisimple factorizable Hopf algebra,
we can associate its Drinfel'd element. Taking the
trace of this element in the regular representation, one obtains
a certain number. As we explain in the talk, this number has many
similarities with the classical Gaussian sum, and in fact coincides
with the classical Gaussian sum for a suitably chosen Hopf algebra.
The talk is based on joint work with Yongchang Zhu.
 Colloquium on Hopf Algebras, Quantum Groups and Tensor Categories
 Title: On the central charge of a factorizable Hopf algebra
 Location: Córdoba, Argentina
 Date: Wednesday, September 2, 2009
 Summary: For a semisimple factorizable Hopf algebra over a field of characteristic zero, we show that the value that an integral takes on the inverse Drinfel'd element differs from the value that it takes on the Drinfel'd element itself at most by a fourth root of unity. This can be reformulated by saying that the central charge of the Hopf algebra is an integer. If the dimension of the Hopf algebra is odd, we show that these two values differ at most by a sign, which can be reformulated by saying that the central charge is even. We give a precise condition on the dimension that determines whether the plus sign or the minus sign occurs. To formulate our results, we use the language of modular data. The talk is based on joint work with Yongchang Zhu.
 Graduate Research Conference in Algebra and Representation Theory
 Title: A survey on the theory of Hopf algebras
 Location: Manhattan, USA
 Date: Sunday, May 24, 2009, and Monday, May 25, 2009
 Summary: A Hopf algebra is an algebra for which
one can form the tensor product of two modules.
For this, one needs a new structure element, the
socalled coproduct. The theory of these algebras
has progressed substantially in the last decade.
We give an overview of the theory of Hopf algebras,
starting from the definition and ending at some of
the most recent developments. Throughout, we emphasize
the analogy with groups; in particular, we will see
what the analogues of Lagrange's theorem and Cauchy's
theorem for Hopf algebras are.
 The Southern Regional Algebra Conference at the University of Colorado at Colorado Springs
 Title: Hopf algebras, FrobeniusSchur indicators, and the modular group
 Location: Colorado Springs, USA
 Date: Sunday, September 28, 2008
 Summary: Every factorizable Hopf algebra leads to a projective representation of the modular group. In the semisimple case, the kernel of this representation is in fact congruence subgroup whose level is determined by the exponent of the Hopf algebra. We explain how generalized FrobeniusSchur indicators can be used to establish this fact.
 First Canadian Hopf algebra conference: the role of Hopf algebras in Noncommutative Geometry
 Title: FrobeniusSchur indicators and congruence subgroups
 Location: Fredericton, Canada
 Date: Saturday, September 6, 2008
 Summary: In a recent joint article with Yongchang Zhu, it was shown
that the kernel of the action of the modular group on the center of a semisimple
factorizable Hopf algebra, which is possibly sometimes only a projective
action, is a congruence subgroup whose level is the exponent of the
Hopf algebra. We give a comprehensive overview over this article.
 AMS Spring Western Sectional Meeting: Special session on Hopf algebras and quantum groups
 Title: The Hopf symbol
 Location: Claremont, USA
 Date: Saturday, May 3, 2008
 Summary: It is a classical result that Gaussian sums transform with the
Jacobi symbol under the action of the Galois group. We explain
in the talk how this fact can be generalized to semisimple factorizable
Hopf algebras: If one turns the group ring of a cyclic group into a factorizable Hopf algebra by endowing it with a nontrivial Rmatrix, the Gaussian sum occurs as the trace of the inverse Drinfel'd element in the regular representation. It now turns out that also for more general factorizable Hopf algebras the trace of the inverse Drinfel'd element transforms under the action of the Galois group in a similar way, namely with a generalization of the Jacobi symbol that we call the Hopf symbol. The talk is based on joint work with Yongchang Zhu.
 AMS Spring Southeastern Sectional Meeting: Special session on actions of quantum algebras
 Title: The congruence subgroup property for factorizable Hopf algebras
 Location: Baton Rouge, USA
 Date: Sunday, March 30, 2008
 Summary:
Consider a factorizable semisimple Hopf algebra over an algebraically
closed field of characteristic zero. If the Drinfel'd element and its
inverse have the same trace in the regular representation, then the
action of the modular group on the center of the Hopf algebra yields not
only a projective, but rather an ordinary linear representation.
We prove that in this case the kernel of this linear representation is
a congruence subgroup of level N, where N is the exponent of the Hopf algebra. To do this, we introduce a generalization of the Jacobi symbol that relates the action of the Galois group to the action of the diagonal matrices in the quotient of the modular group. The talk is based on joint work with Yongchang Zhu.
 First Joint International Meeting between the AMS and the NZMS: Special session on Hopf algebras and quantum groups
 Title: Hopf algebras and congruence subgroups
 Date: Saturday, December 15, 2007
 Location: Wellington, New Zealand
 Summary: We prove that the kernel of the natural action of the modular group on the center of the Drinfel'd double of a semisimple Hopf algebra is a congruence subgroup. To do this, we introduce a class of generalized FrobeniusSchur indicators and endow it with an action of the modular group that is compatible with the original one. The talk is based on joint work with Yongchang Zhu.
 AMS Fall Central Sectional Meeting: Special session on Hopf algebras and related areas
 Title: FrobeniusSchur indicators and their generalizations
 Location: Chicago, USA
 Date: Saturday, October 6, 2007
 Summary:
We introduce a class of generalized FrobeniusSchur indicators
and discuss their applications. The talk is based on joint work
with Yongchang Zhu.
 The Southern Regional Algebra Conference at the University of Louisiana at Lafayette
 Title: The exponent of a Hopf algebra
 Date: Sunday, September 30, 2007
 Location: Lafayette, USA
 Summary:
A Hopf algebra is an algebra for which it is possible to
form the tensor product of two representations. The fact that
it is possible to form the tensor product of two group representations
therefore can be viewed as a consequence of a Hopf structure
on the group algebra. Certain concepts and theorems carry over from
groups to Hopf algebras: We explain how the exponent may be defined in this setting and how Cauchy's theorem looks for Hopf algebras. The talk is based on joint work with Y. Kashina and Y. Zhu.

