Kolloquium Wilhelm Killing

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shupp_01

Kolloquium Wilhelm Killing: Prof. Dr. Piotr Achinger (IMPAN): Homotopy types in algebraic geometry

Donnerstag, 27.06.2019 16:30 im Raum M5
Mathematik und Informatik

Abstract: Algebraic topology studies algebraic invariants of topological spaces, typically identifying spaces which are "homotopy equivalent." Homotopy theory proved essential in the study of topological spaces; when applied to algebraic varieties, its ideas turn out to be even more powerful, as the resulting invariants have far more structure, often coming from either complex analysis (Hodge theory) or arithmetic (an action of a Galois group). In particular, as predicted e.g. by the Hodge conjecture, the Tate conjecture, or Grothendieck?s section conjecture, they should be able to detect algebraic cycles and rational points. Over the field of complex numbers, an algebraic variety gives rise to a nice topological space to which one can apply methods of algebraic topology directly. From the point of view of arithmetic and algebraic geometry over more general fields, it is of key importance to construct algebraically defined topological invariants. Probably the most successful development to this date achieving this goal is the introduction of the etale topology by Artin and Grothendieck, and the etale homotopy type of Artin and Mazur. I will give a gentle introduction to this circle of ideas, explain several ways in which one can associate a homotopy type to an algebraic variety, and discuss how the resulting objects witness phenomena quite foreign to classical algebraic topology of nice topological spaces.



Angelegt am Donnerstag, 21.03.2019 14:34 von shupp_01
Geändert am Montag, 24.06.2019 16:31 von a_schi11
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Kolloquium Wilhelm Killing
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Mathematics Münster
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Kolloquium Wilhelm Killing: Dr. André Hendriques (University of Oxford): Three approaches to conformal field theory

Donnerstag, 04.07.2019 16:30 im Raum M5
Mathematik und Informatik

There exist three mathematical formalizations of the concept of chiral conformal field theory: Vertex operator algebras, Conformal nets, and Segal CFTs. These three notions are expected/conjectured to be equivalent (provided appropriate qualifiers are added). In this overview talk, I will explain, based on examples, what are Vertex operator algebras, Conformal nets, and Segal CFTs. I will describe how one is supposed to go from one formalism to the other, and where the main difficulties lie.



Angelegt am Donnerstag, 21.03.2019 14:35 von shupp_01
Geändert am Dienstag, 16.04.2019 10:44 von shupp_01
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Kolloquium Wilhelm Killing
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Kolloquium Wilhelm Killing: Prof. Dr. Katrin Wendland (Universität Freiburg): Moonshine Phenomena

Donnerstag, 11.07.2019 16:30 im Raum M5
Mathematik und Informatik

Moonshine', in Mathematics, refers to surprising and deep connections between finite group theory and the theory of so-called modular forms. The first known instance of Moonshine is Monstrous Moonshine, where the coefficients of the modular j-function are identified as dimensions of representations of the Monster group. This was first observed by John McKay in 1987; Richard Borcherds received a Fields Medal for his proof of the resulting Moonshine Conjectures in 1998. More than a decade later, Tohru Eguchi, Hiroshi Ooguri and Yuji Tachikawa proposed 'Mathieu Moonshine', which links the largest Mathieu group to topological invariants of K3 surfaces, yielding the Fourier coefficients of a certain elliptic modular form. Conformal field theory turns out to be key to every known instance of moonshine. The talk will give an introduction to solved and unsolved mysteries of these two types of Moonshine.



Angelegt am Donnerstag, 21.03.2019 14:36 von shupp_01
Geändert am Montag, 24.06.2019 10:50 von shupp_01
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Kolloquium Wilhelm Killing
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