Chiral de Rham Complex and Orbifolds
Monday, 3.11.14, 16:15-17:15, Raum 404, Eckerstr. 1
Chow Motives
Tuesday, 4.11.14, 14:00-15:00, Raum 414, Eckerstr. 1
Discrete quasi-Einstein metrics and combinatorial curvature flows in
Tuesday, 4.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Motivated by the definition of combinatorial scalar curvature given by Cooper and Rivin, we introduce a \nnew combinatorial scalar curvature. Then we define \nthe discrete quasi-Einstein metric, which is a combinatorial analogue of the constant scalar curvature metric in smooth case. We find that discrete quasi-Einstein metric is critical point of both the combinatorial Yamabe functional and the quadratic energy functional we defined on triangulated 3-manifolds. We introduce combinatorial curvature flows, including a new type of combinatorial Yamabe flow, to study the discrete quasi-Einstein metrics and prove that the flows produce solutions converging to discrete quasi-Einstein metrics if the initial normalized quadratic energy is small enough. As a corollary, we prove that nonsingular solution of the combinatorial Yamabe flow with nonpositive initial curvatures converges to discrete quasi-Einstein metric. The proof relies on a careful analysis of the discrete dual-Laplacian, which we interpret as the Jacobian matrix of curvature map.
Chow Motives
Wednesday, 5.11.14, 10:00-11:00, Raum 403, Eckerstr. 1
Basic Notions: Forcing
Wednesday, 5.11.14, 16:30-17:30, Raum 404, Eckerstr. 1
Chow Motives
Thursday, 6.11.14, 12:00-13:00, Raum 404, Eckerstr. 1
Thursday, 6.11.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Overconvergent de Rham-Witt connections
Friday, 7.11.14, 10:15-11:15, Raum 404, Eckerstr. 1
For a smooth scheme over a perfect field of characteristic p>0, we generalise a definition of Bloch and introduce overconvergent de Rham-Witt connections. This provides a tool to extend the comparison morphisms of Davis, Langer and Zink between overconvergent de Rham-Witt cohomology and Monsky-Washnitzer respectively rigid cohomology to coefficients.\nIn this talk I will describe the main constructions and explain how the comparison theorems can be adapted.
Gauged Linear Sigma Models, disk partition function and nonabelian matrix factorizations
Monday, 10.11.14, 16:15-17:15, Raum 404, Eckerstr. 1
I will explain how the supersymmetric disk partition function Z of gauged linear sigma models relates to the central charge of objects in the category of B-branes of a Calabi-Yau (CY). The advantage of this approach is that Z provides an expression at every point in the quantum corrected moduli space of the CY. The B-branes in these models are realized naturally as matrix factorizations, equivariant under the gauge group. I will explain how to relate them to more familiar objects such as coherent sheaves on the CY and show examples, if time alllows.
The Ricci Flow on Surfaces
Tuesday, 11.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Y-c.c. and Y-proper forcings
Wednesday, 12.11.14, 16:30-17:30, Raum 404, Eckerstr. 1
Dirac Operator for Harish-Chandra modules
Thursday, 13.11.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Variation of Moduli Spaces of Gieseker-Maruyama-semistable sheaves
Friday, 14.11.14, 10:15-11:15, Raum 404, Eckerstr. 1
Moduli spaces of semistable sheaves over polarized projective manifolds of dimensions greater than one have been constructed by Gieseker and Maruyama using Geometric Invariant Theory. In dimension two their variation as the polarization varies has been thoroughly investigated. In dimension three already irrational polarizations appear in an essential way, for which not even the construction of a corresponding moduli space was known. \nIn this talk we present a joint work together with Daniel Greb and Julius Ross in which we introduce and study a new stability notion allowing to solve the construction and variation problems at least in dimension three. The new moduli spaces are obtained as subschemes in moduli spaces of representations of appropriate quivers.
tba
Monday, 17.11.14, 16:15-17:15, Raum 404, Eckerstr. 1
Differntial Harnack inequality along the Ricci flow
Tuesday, 18.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Representing sets of cofinal branches as continuous images
Wednesday, 19.11.14, 16:30-17:30, Raum 404, Eckerstr. 1
Let \(\bkappa\) be an infinite cardinal and \(T\) be a tree of height \(\bkappa\). We equip the set \([T]\) of all branches of length \(\bkappa\) through \(T\) with the topology whose basic open subsets are sets of all branches containing a given node in \(T\). Given a cardinal \(\bnu\), we consider the question whether \([T]\) is equal to a continuous image of the tree of all functions \(s:\balpha\blongrightarrow\bnu\) with \(\balpha<\bkappa\). This is joint work with Philipp Schlicht.\n\n
Modellierung von Solvenz- und Liquiditätsrisiken
Thursday, 20.11.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Wir entwickeln ein strukturelles Kreditrisikomodell, das sowohl Solvenz- \nals auch Liquiditätsrisiken berücksichtigt. In einem solchen Modell kann \nder Einfluss von Liquiditätsrisiken, die aus der Finanzierungsstruktur \neines Unternehmens entstehen, auf die Ausfallwahrscheinlichkeit des \nUnternehmens untersucht werden. Dabei nehmen wir an, dass das \nUnternehmen seine risikobehafteten Aktiva durch kurzfristiges und \nlangfristiges Fremdkapital finanziert. Kurzfristiges Fremdkapital kann \neine diskrete oder eine gestaffelte Tenorstruktur aufweisen und kann an \nden jeweiligen Fälligkeitsterminen verlängert werden. Wir zeigen, dass \nes eine eindeutige Schranke gibt, so dass kurzfristiges Fremdkapital \nnicht verlängert wird, wenn der Wert der Aktiva des Unternehmenes unter \ndiese Schranke fällt. Basierend auf dieser endogenen Schranke und einer \nexogenen Insolvenzschranke kann die Ausfallwahrscheinlichkeit in eine \nInsolvenz- und eine Illiquiditätskomponente zerlegt werden.\n
Degenerate flags and Schubert varieties
Friday, 21.11.14, 10:15-11:15, Raum 404, Eckerstr. 1
Introduced in 2010 by E. Feigin, degenerate flag varieties are degenerations of flag manifolds. It has been proven that, in type A and C, they share many properties with Schubert variety. In this talk I will first recall the classical setting (flag and Schubert varieties) and then discuss joint work with Cerulli Irelli, where we prove a surprising fact about degenerate flags.
Integrable Systems via Lax equations
Monday, 24.11.14, 16:15-17:15, Raum 404, Eckerstr. 1
Many integrable systems can be formulated as a so-called Lax equation. In this talk, we will review the up to now well-known construction which relates such integrable systems to algebraic geometry. If time permits, we also discuss some further directions due to Donagi, McDaniel-Smolinsky and others leading to decomposition of spectral covers and Prym-Tyurin varieties.
Bochner-Weitzenboeck formula and Harnack estimates for Finsler manifolds
Tuesday, 25.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Overview of the generalized combinatorial cardinal characteristics
Wednesday, 26.11.14, 16:30-17:30, Raum 404, Eckerstr. 1
I will talk about how the combinatorial cardinal characteristics\nreviewed in [Blass, Combinatorial Cardinal Characteristics of the\nContinuum] can be generalized to uncountable cardinals kappa and what is\nknown about consistency results for them.\n\n
Mathematical Knowledge Management and Information Retrieval: Transcending the One-Brain-Barrier
Thursday, 27.11.14, 13:00-14:00, Raum 404, Eckerstr. 1
We present the emerging discipline of Mathematical Knowledge Management (MKM), which studies the possibility of computer-supporting and even automating the representation, cataloguing, retrieval, refactoring, plausibilization, change propagation and in some cases even application of mathematical knowledge.\n\nWe focus on theory graph technology here, which supports modular and thus space-efficient representations of mathematical knowledge and allows MKM systems to achieve a limited mathematical literacy that is necessary to complement the abilities of human mathematicians and thus to enhance their productivity.
The Software Development Approach in Pure Mathematics
Thursday, 27.11.14, 14:45-15:45, Raum 404, Eckerstr. 1
Taking into account that proofs are programs (made precise by type theory), and the move from documents to knowledge models (MKM), we look at some software tools that help pure mathematics and propose the development of new tools by semi-formalisation of mathematical content.
The proof assistant Isabelle
Thursday, 27.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Isabelle is an interactive theorem prover. In other words: It is an editor for mathematical text that tell you where you might be wrong wrong (or just sloppy), but also where you are right.\n\nWe see Isabelle in action, proving a simple theorem. This will not teach you how to use Isabelle, but it will hopefully make you want to learn it. We also discuss its advantages and disadvantages over other theorem provers.
Thursday, 27.11.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
(Homotopy) Type Theory
Friday, 28.11.14, 10:00-11:00, Raum 404, Eckerstr. 1
We will introduce the basic formalism of dependent type theory with identity types and its standard informal interpretations: logical (via the Curry-Howard isomorphism), set-theoretical/categorial and homotopy theoretical.
Ample subschemes and two conjectures of Hartshorne
Friday, 28.11.14, 10:15-11:15, Raum 127, Eckerstr. 1
The talk will survey geometric properties of subvarieties and cycles with\nvarious positivity properties. We also discuss related conjectures of\nHartshorne and Peternell about subvarieties with ample normal bundle.
Homotopy Type Theory
Friday, 28.11.14, 11:30-12:30, Raum 404, Eckerstr. 1
We present the formal interpretation of type theory in model categories and discuss the univalence axiom and the usability of type theory as a tool and foundation for mathematics.
Verifying (Homotopy) Type Theory in Agda
Friday, 28.11.14, 14:00-15:00, Raum 404, Eckerstr. 1
We will look at some basic definitions and proofs in Agda with a focus on Homotopy Type Theory. Another aim is discussing some obstacles that occur while learning how to formalize Homotopy Type Theory in Agda.