Das Mathematische Kolloquium ist eine gemeinsame wissenschaftliche Veranstaltung des gesamten Mathematischen Instituts. Es steht allen Interessierten offen und richtet sich neben den Mitgliedern und Mitarbeitern des Instituts auch an die Studierenden. Das Kolloquium findet dreimal im Semester am Donnerstag um 17:00 s.t. im Hörsaal II, Albertstr. 23b statt. Danach (gegen 16:15) gibt es Kaffee und Kekse, zu dem der vortragende Gast und alle Besucher eingeladen sind.
Hamiltonian mechanics and holomorphic curves: a round trip
Thursday, 18.4.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Symplectic geometry has its origins in the Hamiltonian\nformulation of classical mechanics. Holomorphic curves are\nthe most important tools to study global properties of\nsymplectic manifolds. In my talk I will provide a return\nticket from holomorphic curves back to Hamiltonian\nmechanics. Translating certain geometric properties of\nholomorphic curves into algebra, I will show that we\nnaturally arrive at Hamiltonian mechanics on an\ninfinite-dimensional (singular) phase space. In the\nsimplest case, this leads to the famous integrable system\ndescribing waves in shallow water.
Geometrie und Dynamik diskreter Untergruppen von halbeinfachen Liegruppen - Dynamics and geometry of discrete subgroups or semi-simple Lie groups
Thursday, 25.4.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
In diesem Vortrag werde ich einige geometrische und dynamische Eigenschaften von diskreten Untergruppen in halbeinfachen Liegruppen (z.B. SL(n,R)) diskutieren. Ich werde hierbei insbesondere Untergruppen betrachten, die im Zusammenhang mit höhere Teichmuellertheorie auftreten.\n\nI will discuss dynamical and geometric properties of discrete subgroups of Lie groups (e.g. SL(n,R)). A special focus will lie on subgroups which arise in connection with higher Teichmüller theory.
Thursday, 2.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 9.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 16.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 23.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 30.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
On the invariant universality property
Thursday, 6.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
The notion of Borel reducibility has been introduced as a tool for measuring the\ntopological complexity of analytic equivalence relations and quasi-orders, an abstract class of\nobjects which includes many relations from various areas of mathematics such as: isomorphism and\n(algebraic) embeddability between countable structures from model theory, homeomorphism and\ntopological embeddability between continua from general topology, isometry and isometric\nembeddability between Polish spaces from analysis, linear isometry and linear isometric\nembeddability between separable Banach spaces from functional analysis, and many others.\nIntuitively, an analytic quasi-order as above is called invariantly universal if it contains in a\nnatural way a Borel-isomorphic copy of any other analytic quasi-order. In this talk, building on\nprevious work of Louveau and Rosendal we will show that most of the analytic quasi-orders which\nare sufficiently complicated (that is: Borel-complete) are in fact invariantly universal. For\nexample, one can show that for every analytic quasi-order R there is a Borel collection C of\nseparable Banach spaces closed under linear isometry such that the relation of linear isometric\nembeddability on C is Borel-isomorphic to R.\n
Thursday, 13.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 20.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Some Reflections on the Continuum Hypothesis
Thursday, 27.6.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
The Continuum Problem is whether there is a set of reals whose cardinality is\nstrictly between the cardinality of the integers and the reals. This was the first\nproblem on Hilbert’s famous list and it turned out to be undecidable by the usual\naxiom systems for Set Theory. The results of Goedel and Cohen tell us that the\naxioms give very little information about the relative size of the set of integers and\nthe set of reals. Goedel’s conjecture that strong axioms of infinity will settle the\nproblem turned out to be false. Is this the end of the story?\nIn this talk we shall survey some of current approaches of trying to give a mean-\ningful answer to the problem, in spite of its independence. Two direction of research\nwe shall concentrate on will be forcing axioms and the theory of universally Baire\nsets of reals.\n
Thursday, 4.7.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 11.7.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 18.7.13, 17:00-18:00, Hörsaal II, Albertstr. 23b