Conical spherical metrics: Lecture III
Thursday, 1.2.18, 13:00-14:00, SR 403, Eckerstr. 1
A multi-scale approach to reaction-diffusion processes in domains with microstructure
Thursday, 1.2.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multi-scale problems, which has proven reliable for obtaining feasible macroscopic models rigorously, is the method of periodic homogenisation. \n\nThe talk will give an introduction to multi-scale modelling of physico-chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, certain aspects particularly relevant in upscaling reaction-diffusion processes in biological cells will be discussed together with their applications.
Conical spherical metrics: Lecture IV
Friday, 2.2.18, 10:15-11:15, Raum 404, Eckerstr. 1
Probing Solar and Stellar Physics by Helio- and Asteroseismology
Friday, 2.2.18, 14:15-15:15, Hörsaal II, Albertstr. 23b
The Sun and the stars are subject to sound waves that probe their interiors. Observations of these stellar oscillations have emerged as a powerful tool to gain information on the processes inside the Sun and the stars.\n\nThrough helio- and asteroseismology detailed inferences of the stellar internal structure and of the physical processes inside stars can be obtained. In particular, helioseismology allows studying sunspots and other magnetic active areas on the Sun, which have an important impact on our technological society through potentially harmful solar eruptions.\n\nHowever, a complete understanding of the Sun, and in particular of its magnetism, can only be obtained by understanding the internal structure and properties of the stars in general. Asteroseismology offers solving this problem.
Various flavours of Chern classes
Monday, 5.2.18, 16:15-17:15, Raum 404, Eckerstr. 1
Characteristic classes of vector bundles provide an important tool to study these geometric objects using techniques from algebraic topology, i.e. cohomology. In my talk I will give an introduction to Chern classes, which are characteristic classes of complex vector bundles. I will present several points of view onto this topic, each emphasising a certain aspect of Chern classes. This will help to understand the significance of this machinery.
Hyperbolic AMD mass
Tuesday, 6.2.18, 16:15-17:15, Raum 404, Eckerstr. 1
This talk is about the hyperboic AMD mass.\n1. The background\n2. Its definition\n3. Its well-definedness and its invariance.\n4. A generalization.\n
tba
Wednesday, 7.2.18, 16:30-17:30, Raum 404, Eckerstr. 1
Compactness and reflection in mathematics
Wednesday, 7.2.18, 16:30-17:30, Raum 404, Eckerstr. 1
Abstract: One of the most fruitful research area in set theory is the study of the so-called reflections principles'. Roughly speaking, by reflection principle we mean a combinatorial statement of the following form: given a structure S (e.g. a stationary set, a tree, a graph, a groups ...) and a property P of the structure, the principle establishes that there exists a smaller substructure of S that satisfies the same property P. Compactness is dual to reflection, namely bycompactness property' we mean roughly a statement of the following form: given a structure S and a property P in the language of the structure, if every smaller substructure has the property P, then S satisfies P as well. \n\nMany interesting mathematical problems can be formulated as compactness problems; for instance, there is an extensive literature on the compactness problem for the property of being a free group: given a group G, suppose that every small subgroup (i.e. of smaller size) is free, is G itself free? This problem is independent from ZFC and the answer depends on the cardinality of the group. \n\nStrong forms of reflection are typically associated with large cardinals axioms, which therefore imply interesting compactness results. There is a tension between large cardinals axioms and the axiom of constructibility V=L at the level of reflection: on the one hand, large cardinals typically imply reflection properties, on the other hand L satisfies the square principles which are anti-reflection properties. Two particular cases of reflection received special attention, the reflection of stationary sets and the tree property. We will discuss the interactions between these principles and a version of the square due to Todorcevic. This is a joint work with Menachem Magidor and Yair Hayut. \n\n
Compactness and reflection
Wednesday, 7.2.18, 17:30-18:30, Raum 404, Eckerstr. 1
tba
Thursday, 8.2.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Resolution of singularities of the cotangent sheaf of a singular variety
Friday, 9.2.18, 10:30-11:30, Hörsaal FRIAS, Albertsstr. 19
The subject of the talk is resolution of singularities of differential forms on an algebraic or analytic variety. We address the problem of finding a resolution of singularities \(\bsigma : X \bto X_0 \) of a singular algebraic or analytic variety \(X_0\) such that the pulled back cotangent sheaf of \(X_0\) (i.e., the pull-back of the Kahler differential forms defined in \(X_0\)) is given, locally in \(X\), by monomial differential forms (with respect to a suitable coordinate system). This problem is related with monomialization of maps, the \(L^2\) cohomology of singular varieties and reduction of singularities of vector-fields. In a work in collaboration with Bierstone, Grandjean and Milman, we give a positive answer to the problem when \(dim\b, X_0 \bleq 3\).
On the topology of smooth hypersurfaces
Friday, 9.2.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
To what extent the Chern class of a divisor (in singular\ncohomology) determines its topology?\nDiscussion of a conjecture by Totaro concerning the topology\nof smooth hypersurfaces on projective manifolds.
Algebraic curves and modular forms of low degree
Friday, 23.2.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
For genus 2 and 3 modular forms are intimately connected with\nthe moduli of curves of genus 2 and 3. We give an explicit way to\ndescribe such modular forms for genus 2 and 3\nusing invariant theory and give some applications.\nThis is based on joint work with Fabien Clery and Carel Faber.\n
The McKay correspondence and the eta-invariant
Monday, 26.2.18, 14:00-15:00, Raum 404, Eckerstr. 1
GPSD 2018
Tuesday, 27.2.18, 09:00-10:00, Institusviertel
GPSD 2018
Wednesday, 28.2.18, 09:00-10:00, Institusviertel