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Calendar

Events at the Department of Mathematical Sciences.

• 2 May 2017, 15:15-16:15

Algebra/Topology Seminar by Joachim Kock

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 infinity-groupoids 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 up-to-homotopy composition, the new condition expresses decomposition.  The role of vector spaces is played by slices over infinity-groupoids, eventually with homotopy finiteness conditions imposed.  To any decomposition space, there is associated an incidence (co)algebra with coefficients in infinity-groupoids, which satisfies an objective Möbius inversion principle in the style of Lawvere-Menni, 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 S-construction (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 2-Segal space of Dyckerhoff-Kapranov.)

• 3 May 2017, 13:15-17:35

Øresundsseminar

The Oresund seminar will take place in Lund May 3, 2017.

• 5 May 2017, 13:15

Seminar in applied mathematics and statistics

Søren Hauberg: Diffeomorphisms for Dummies and Augmentations for Awesommies

• 5 May 2017, 14:15

Wind Farm Layout Optimization With Non-Linear Wake effects

Specialeforsvar ved Christoffer Larsen

• 5 May 2017, 15:15-16:00

What is forcing?

David Schrittesser will explain what forcing is. Forcing is a technique used to prove independence and consistency results in set theory.

• 8 May - 11 May 2017

Masterclass: Cohomology of arithmetic groups

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.

• 8 May 2017, 10:00-11:00

Masterclass Lecture by Andy Putman

Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the high-dimensional 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 Borel-Serre bordification, Bieri-Eckmann duality, the structure of the Steinberg module, and the high-dimensional cohomology of these groups.

• 8 May 2017, 11:30-12:30

Masterclass Lecture by Harald Grobner

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 epoch-making work of J. Franke that this identication of group-cohomology 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 ζ-functions 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 far-reaching 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.

• 8 May 2017, 15:15-16:15

Algebra/Topology Seminar by Herbert Gangl

Talk by Herbert Gangl (Durham University) Title: Zagier's polylogarithm conjecture revisited Abstract: In the early nineties, Goncharov proved the weight 3 case of Zagier's Conjecture stating that the special value $\zeta_F(3)$ of a number field $F$ is essentially expressed as a determinant of trilogarithm values taken in that field. He also envisioned a vast--partly conjectural--programme of how to approach the conjecture for higher weight. We can remove one important obstacle in weight~4 by solving one of Goncharov's conjectures. It further allows us to deduce a functional equation for $Li_4$ in four variables as one expects to enter in a more explicit definition of $K_7(F)$.

• 9 May 2017, 10:00-11:00

Masterclass Lecture II by Andy Putman

Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the high-dimensional 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 Borel-Serre bordification, Bieri-Eckmann duality, the structure of the Steinberg module, and the high-dimensional cohomology of these groups.

• 9 May 2017, 11:30-12:30

Masterclass Lecture II by Harald Grobner

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 epoch-making work of J. Franke that this identication of group-cohomology 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 ζ-functions 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 far-reaching 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.

• 9 May 2017, 14:00-15:00

Masterclass Lecture by Orsola Tommasi

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 » Read more

• 10 May 2017, 10:00-11:00

Masterclass Lecture III by Andy Putman

Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the high-dimensional 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 Borel-Serre bordification, Bieri-Eckmann duality, the structure of the Steinberg module, and the high-dimensional cohomology of these groups.

• 10 May 2017, 11:30-12:30

Masterclass Lecture III by Harald Grobner

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 epoch-making work of J. Franke that this identication of group-cohomology 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 ζ-functions 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 far-reaching 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.

• 10 May 2017, 12:00-13:00

QLunch: TBA

Speaker: Nathan Harshman, Visiting Associate Professor, Aarhus University.

• 11 May 2017, 10:00-11:00

Masterclass Lecture IV by Andy Putman

Lecture in Masterclass: Cohomology of arithmetic groups by Andy Putman (Notre Dame) Title: Buildings, duality, and the high-dimensional 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 Borel-Serre bordification, Bieri-Eckmann duality, the structure of the Steinberg module, and the high-dimensional cohomology of these groups.

• 11 May 2017, 11:30-12:30

Masterclass Lecture IV by Harald Grobner

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 epoch-making work of J. Franke that this identication of group-cohomology 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 ζ-functions 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 far-reaching 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.

• 11 May 2017, 14:00-15:00

Masterclass Lecture by Alexander Kupers

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, Elbaz-Vincent and Martinet using the techniques discussed in the masterclass.

• 15 May - 19 May 2017

Master Class on Exotic Phases of Matter

The discovery of exotic phases of matters, which has been awarded with a Nobel-prize in 2016, remains one of the most active and important research fields in quantum many-body theory.

• 15 May 2017, 12:45

Joint Number theory/Geometry and Analysis seminar

Speaker: Yiannis N. Petridis (UCL/UCPH). Title: Arithmetic Statistics of modular symbols.

• 16 May 2017, 11:15

Cirelson Bounds, Rigidity and Robustness of Non-Local Games

Specialeforsvar ved Nicholas Gauguin Houghton-Larsen

• 17 May 2017, 14:15

Subexponential Distributions

Specialeforsvar ved Michael Skibsted

• 17 May 2017, 15:15-16:15

Operator algebra seminar

Seminar talk given by Rasmus Bentmann (University of Göttingen)

• 22 May 2017, 13:30-14:30

Algebra/Topology Seminar by Simona Settepanella

Talk by Simona Settepanella (Hokkaido University) Title and Abstract: TBA

• 22 May 2017, 15:15-16:15

Algebra/Topology Seminar by Cristiano Spotti

Talk by Cristiano Spotti (Aarhus) Title and Abstract: TBA