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 Yetter-Drinfel'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: Yetter-Drinfel'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 Yetter-Drinfel'd Hopf algebras
  • Location: Sofia, Bulgaria
  • Date: Thursday, July 14, 2016
  • Summary

• Brauer Groups, Hopf Algebras and Monoidal Categories
  • Title: Cores in Yetter-Drinfel'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: Yetter-Drinfel'd Hopf algebras and their extensions
  • Location: Chicago, USA
  • Date: Sunday, October 4, 2015
  • Summary

• Algebraic Groups and Lie Algebras
  • Title: Yetter-Drinfel'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 Yetter-Drinfel'd Hopf algebras
  • Location: Porto, Portugal
  • Date: Thursday, June 11, 2015
  • Summary

• New Trends in Hopf Algebras and Tensor Categories
  • Title: Triviality in Yetter-Drinfel'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 Yetter-Drinfel'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 Yetter-Drinfel'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 Yetter-Drinfel'd Hopf algebras
  • Location: Halifax, Canada
  • Date: Sunday, October 19, 2014
  • Summary

• The Southern Regional Algebra Conference at Auburn University-Montgomery
  • Title: Yetter-Drinfel'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 quasi-Hopf algebras and ribbon quasi-Hopf 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: Yetter-Drinfel'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: Quasi-Hopf 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, Eilenberg-MacLane 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 University-Montgomery
  • Title: Hopf algebras and Gaussian sums
  • Date: Friday, March 26, 2010
  • Location: Montgomery, USA
  • Summary: With the R-matrix 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 so-called 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, Frobenius-Schur 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 Frobenius-Schur indicators can be used to establish this fact.

• First Canadian Hopf Algebra Conference: The Role of Hopf Algebras in Noncommutative Geometry
  • Title: Frobenius-Schur 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 R-matrix, 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 Frobenius-Schur 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: Frobenius-Schur indicators and their generalizations
  • Location: Chicago, USA
  • Date: Saturday, October 6, 2007
  • Summary: We introduce a class of generalized Frobenius-Schur 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.

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• Last modification: July 27, 2019