Events at the Centre for Symmetry and Deformation.

2 May 2017,
15:1516:15
Talk by Joachim Kock (Universitat Autònoma de Barcelona) Title: Decomposition spaces, incidence algebras, and Möbius inversion Abstract: I'll survey recent work with Imma Gálvez and Andy Tonks developing a homotopy version of the theory of incidence algebras and Möbius inversion. The 'combinatorial objects' playing the role of posets and Möbius categories are decomposition spaces, simplicial infinitygroupoids satisfying an exactness condition weaker than the Segal condition, expressed in terms of generic and free maps in Delta. Just as the Segal condition expresses uptohomotopy composition, the new condition expresses decomposition. The role of vector spaces is played by slices over infinitygroupoids, eventually with homotopy finiteness conditions imposed. To any decomposition space, there is associated an incidence (co)algebra with coefficients in infinitygroupoids, which satisfies an objective Möbius inversion principle in the style of LawvereMenni, provided a certain completeness condition is satisfied, weaker than the Rezk condition. Generic examples of decomposition spaces beyond Segal spaces are given by the Waldhausen Sconstruction (yielding Hall algebras) and by Schmitt restriction species, and many examples from classical combinatorics admit uniform descriptions in this framework.(The notion of decomposition space is equivalent to the notionof unital 2Segal space of DyckerhoffKapranov.)
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8 May  11 May 2017
The Masterclass will consist of two lecture series by Andy Putman and Harald Grobner, as well as a number of contributed talks about current research. See here for more information.
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8 May 2017,
10:0011:00
Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the highdimensional cohomology of arithmetic groups Abstract: I will discuss topological results about the cohomology of arithmetic groups, focusing for simplicity on the group SL(n,Z). Topics include the BorelSerre bordification, BieriEckmann duality, the structure of the Steinberg module, and the highdimensional cohomology of these groups.
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8 May 2017,
11:3012:30
Lecture in Masterclass: Cohomology of arithmetic groups by Harald Grobner (Universität Wien) Title: Cohomological automorphic forms: A survey based on examples. Abstract: In this lecture series we will study the cohomology of arithmetic groups through the theory of automorphic forms. Firstly conjectured by A. Borel and G. Harder, the cohomology H^q(Γ, E) of an arithmetic (congruence) subgroup Γ of a connected reductive group G is isomorphic to the relative Lie algebra cohomology of a space of automorphic forms on G. It is really due to epochmaking work of J. Franke that this identication of groupcohomology and automorphic cohomology is now known in full generality. This connection of automorphic forms with the cohomology of arithmetic groups is the deep source of a highly interesting mélange of ideas, approaches and moreover possible applications. It turns out that cohomological automorphic forms i.e., automorphic forms contributing to the cohomology H^q(Γ, E) of some arithmetic group Γ as above play the key role in an extremely rich area of mathematical problems: To mention one of their highlights, the analysis of ζfunctions and their generalizations. This lecture series will (try to) put a spotlight on (i) the problems connected with the very study of H^q(Γ, E) by cohomological automorphic forms, as well as (ii) on some of the farreaching applications, mentioned above. As the title suggests, we will do this based on a selection of interesting examples, while we try to avoid the huge backlock of the general theory.
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8 May 2017,
15:1516:15
Talk by Herbert Gangl (Durham University) Title and Abstract: TBA
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9 May 2017,
10:0011:00
Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the highdimensional cohomology of arithmetic groups Abstract: I will discuss topological results about the cohomology of arithmetic groups, focusing for simplicity on the group SL(n,Z). Topics include the BorelSerre bordification, BieriEckmann duality, the structure of the Steinberg module, and the highdimensional cohomology of these groups.
» Read more

9 May 2017,
11:3012:30
Lecture in Masterclass: Cohomology of arithmetic groups by Harald Grobner (Universität Wien) Title: Cohomological automorphic forms: A survey based on examples. Abstract: In this lecture series we will study the cohomology of arithmetic groups through the theory of automorphic forms. Firstly conjectured by A. Borel and G. Harder, the cohomology H^q(Γ, E) of an arithmetic (congruence) subgroup Γ of a connected reductive group G is isomorphic to the relative Lie algebra cohomology of a space of automorphic forms on G. It is really due to epochmaking work of J. Franke that this identication of groupcohomology and automorphic cohomology is now known in full generality. This connection of automorphic forms with the cohomology of arithmetic groups is the deep source of a highly interesting mélange of ideas, approaches and moreover possible applications. It turns out that cohomological automorphic forms i.e., automorphic forms contributing to the cohomology H^q(Γ, E) of some arithmetic group Γ as above play the key role in an extremely rich area of mathematical problems: To mention one of their highlights, the analysis of ζfunctions and their generalizations. This lecture series will (try to) put a spotlight on (i) the problems connected with the very study of H^q(Γ, E) by cohomological automorphic forms, as well as (ii) on some of the farreaching applications, mentioned above. As the title suggests, we will do this based on a selection of interesting examples, while we try to avoid the huge backlock of the general theory.
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9 May 2017,
14:0015:00
Lecture in Masterclass: Cohomology of arithmetic groups by Orsola Tommasi (Chalmers University of Technology and University of Gothenburg) Title: Cohomological stabilization of toroidal compactifications of A_gAbstract: By a classical result of Borel, the cohomology of the symplectic group Sp(2g,Z) stabilizes in degree k
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10 May 2017,
10:0011:00
Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the highdimensional cohomology of arithmetic groups Abstract: I will discuss topological results about the cohomology of arithmetic groups, focusing for simplicity on the group SL(n,Z). Topics include the BorelSerre bordification, BieriEckmann duality, the structure of the Steinberg module, and the highdimensional cohomology of these groups.
» Read more

10 May 2017,
11:3012:30
Lecture in Masterclass: Cohomology of arithmetic groups by Harald Grobner (Universität Wien) Title: Cohomological automorphic forms: A survey based on examples. Abstract: In this lecture series we will study the cohomology of arithmetic groups through the theory of automorphic forms. Firstly conjectured by A. Borel and G. Harder, the cohomology H^q(Γ, E) of an arithmetic (congruence) subgroup Γ of a connected reductive group G is isomorphic to the relative Lie algebra cohomology of a space of automorphic forms on G. It is really due to epochmaking work of J. Franke that this identication of groupcohomology and automorphic cohomology is now known in full generality. This connection of automorphic forms with the cohomology of arithmetic groups is the deep source of a highly interesting mélange of ideas, approaches and moreover possible applications. It turns out that cohomological automorphic forms i.e., automorphic forms contributing to the cohomology H^q(Γ, E) of some arithmetic group Γ as above play the key role in an extremely rich area of mathematical problems: To mention one of their highlights, the analysis of ζfunctions and their generalizations. This lecture series will (try to) put a spotlight on (i) the problems connected with the very study of H^q(Γ, E) by cohomological automorphic forms, as well as (ii) on some of the farreaching applications, mentioned above. As the title suggests, we will do this based on a selection of interesting examples, while we try to avoid the huge backlock of the general theory.
» Read more

11 May 2017,
10:0011:00
Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the highdimensional cohomology of arithmetic groups Abstract: I will discuss topological results about the cohomology of arithmetic groups, focusing for simplicity on the group SL(n,Z). Topics include the BorelSerre bordification, BieriEckmann duality, the structure of the Steinberg module, and the highdimensional cohomology of these groups.
» Read more

11 May 2017,
11:3012:30
Lecture in Masterclass: Cohomology of arithmetic groups by Harald Grobner (Universität Wien) Title: Cohomological automorphic forms: A survey based on examples. Abstract: In this lecture series we will study the cohomology of arithmetic groups through the theory of automorphic forms. Firstly conjectured by A. Borel and G. Harder, the cohomology H^q(Γ, E) of an arithmetic (congruence) subgroup Γ of a connected reductive group G is isomorphic to the relative Lie algebra cohomology of a space of automorphic forms on G. It is really due to epochmaking work of J. Franke that this identication of groupcohomology and automorphic cohomology is now known in full generality. This connection of automorphic forms with the cohomology of arithmetic groups is the deep source of a highly interesting mélange of ideas, approaches and moreover possible applications. It turns out that cohomological automorphic forms i.e., automorphic forms contributing to the cohomology H^q(Γ, E) of some arithmetic group Γ as above play the key role in an extremely rich area of mathematical problems: To mention one of their highlights, the analysis of ζfunctions and their generalizations. This lecture series will (try to) put a spotlight on (i) the problems connected with the very study of H^q(Γ, E) by cohomological automorphic forms, as well as (ii) on some of the farreaching applications, mentioned above. As the title suggests, we will do this based on a selection of interesting examples, while we try to avoid the huge backlock of the general theory.
» Read more

11 May 2017,
14:0015:00
Lecture in Masterclass: Cohomology of arithmetic groups by Harald Grobner (Universität Wien) Title: Computing K_8(Z) Abstract: We explain how to prove a result announced by Dutour, ElbazVincent and Martinet using the techniques discussed in the masterclass.
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15 May 2017,
12:45
Speaker: Yiannis N. Petridis (UCL/UCPH). Title: Arithmetic Statistics of modular symbols.
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17 May 2017,
15:1516:15
Seminar talk given by Rasmus Bentmann (University of Göttingen)
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22 May 2017,
13:3014:30
Talk by Simona Settepanella (Hokkaido University) Title and Abstract: TBA
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22 May 2017,
15:1516:15
Talk by Cristiano Spotti (Aarhus) Title and Abstract: TBA
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24 May 2017,
15:1516:15
Seminar talk given by Elizabeth Gillaspy (University of Muenster)
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26 June  30 June 2017
Masterclass with Matthew Morrow (JussieuParis) and Thomas Nikolaus (MPI Bonn).
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5 August  6 August 2017
A miniworkshop in the weekend leading up to the Young Mathematicians in C*Algebras conference where all women participating in the YMC*A are invited to speak.
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7 August  11 August 2017
The conference will feature minicourses by Kate Juschenko (Northwestern) and Guoliang Yu (Texas A&M) alongside many contributed talks by participants.
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16 October  20 October 2017
Masterclass with lectures by Toke Meier Carlsen (Faroe Islands) and Xin Li (Queen Mary University of London).
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