see program
Donnerstag, 11.4.24, 09:50-10:50, Basel, Hörsaal 120 in Kollegienhaus (Petersplatz 1)
Minimal geodescis
Montag, 22.4.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
A geodesic \(c:\bmathbb{R}\bto M\) is called minimal if a lift to the universal covering globally minimizes distance. On the \(2\)-dimensional torus with an arbitrary Riemannian metric there are uncountably many minimal geodesic. In dimension at least \(3\), there may be very few minimal geodesics. Let us assume that \(M\) is closed. In 1990 Victor Bangert has shown that the number of geometrically distinct minimal geodesics is bounded below by the first Betti number \(b_1\).\n\nIn joint work with Clara Löh, we improve Bangert's lower bound and we show that this number is at least \(b_1^2+2b_1\).\n\nThe talk will have many ties to previous research done in Freiburg many years ago: to the research of Victor Bangert, to the Diploma thesis I have written in Freiburg in 1994 in Bangert's group, to the research of the younger Burago, when he was\na long term guest in Freiburg and other aspects.\n
Herausforderungen beim Lernen von Bruchzahlen: Größenvorstellungen aufbauen, Konzeptwechsel unterstützen, Bias vermeiden
Dienstag, 23.4.24, 18:30-19:30, Hörsaal II, Albertstr. 23b
Beim Übergang von den ganzen Zahlen zu den Bruchzahlen müssen Lernende einen Konzeptwechsel (Conceptual Change) vollziehen, da manche der von den ganzen Zahlen vertrauten Eigenschaften ihre Allgemeingültigkeit verlieren. Dies führt zu typischen Schwierigkeiten und kognitivem Bias bei bestimmten Aufgabenstellungen. \nIm Vortrag werden Studien vorgestellt, in denen neben Aufgabenbearbeitungen auch Reaktionszeiten und Blickbewegungen gemessen wurden, um Denkprozesse genauer zu beschreiben. Ferner wird eine Interventionsstudie vorgestellt, in der untersucht wurde, inwieweit der Aufbau von Größenvorstellungen für Bruchzahlen gezielt gefördert werden kann und zu einer Reduktion von Bias führt. Implikationen für das Unterrichten von Bruchzahlen werden zur Diskussion gestellt\n
On the injectivity and non-injectivity of the \(l\)-adic cycle class maps
Freitag, 26.4.24, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
We study the injectivity of the cycle class map with values in Jannsen's continuous étale cohomology, by using refinements that go through étale motivic cohomology and the ``tame'' version of Jannsen's cohomology. In particular, we use this to show that the Tate and the Beilinson conjectures imply that its kernel is torsion in positive characteristic, and to revisit recent counterexamples to injectivity.\n
Multiplication of BPS states in heterotic torus theories
Montag, 29.4.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
The space of states of an N = 2 superconformal field theory contains an infinite-dimensional subspace of Bogomol'nyi–Prasad–Sommerfield (BPS) states, defined as states with minimal energy given their charge. In particular, they arise in worldsheet theories of strings. In this setting, Harvey and Moore introduced a bilinear map on BPS states.\n\nThis talk presents a mathematically rigorous approach to this construction, which has been considered promising but not properly understood for almost 30 years now. The example used throughout is that of a heterotic string with all but four dimensions compactified on a torus. For this case, the BPS states were claimed to form a Borcherds–Kac–Moody algebra, as introduced in Borcherds' proof of the monstrous moonshine conjectures.\n\nThe first half of the talk, unfortunately, consists in pointing out problems with the proposed construction. The second half will provide more details on selected aspects, such as the existence of a finite-dimensional Lie algebra of massless BPS states.
Two-scale finite element approximation of a homogenized plate model
Dienstag, 30.4.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We study the discretization of a homogenized and dimension reduced model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić in 2014. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proven for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper.
Magnetic skyrmions
Donnerstag, 2.5.24, 15:00-16:00, Hörsaal II, Albertstr. 23b
Stress-mediated growth determines division site morphology of E. Coli
Dienstag, 7.5.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Bacteria are enveloped by a rigid cell wall and replicate by cell division. During the division, the cell wall needs to be drastically reshaped. It is hypothesized that the remodeling process is stress-mediated and driven by the constrictive force of a protein assembly, the Z-ring. We found that a simple large-strain morpho-elastic model can reproduce the experimentally observed shape of the division site during the constriction and septation phases of E. Coli. Our model encapsulates the multiple enzyme-dependent wall restructuring processes into a single modulus. Depending on this parameter, different experimentally known morphologies can be recovered, corresponding either to mutated or wild type cells. In addition, a plausible range\nfor the cell stiffness and turgor pressure was determined by comparing numerical simulations with experimental data on cell lysis and reported cell sacculus deformation experiments.
Modellieren im Mathematikunterricht
Dienstag, 7.5.24, 18:00-19:00, Hörsaal II, Albertstr. 23b
Mathematisches Modellieren ist eine wichtige prozessbezogene Kompetenz, die in Bildungsstandards und Curricula in Deutschland, den USA und vielen anderen Ländern ausgewiesen ist. Im Vortrag werden der Stand der Forschung zu den Teilkompetenzen des Modellierens (unter anderem Verstehen, Mathematisieren und Validieren) vorgestellt und Lernumgebungen präsentiert, die sich förderlich auf die kognitive und motivationale Entwicklung von Schülerinnen und Schülern auswirken.
Informationsveranstaltung zum neuen Studiengang "M.Sc. Mathematics in Data and Technology"
Donnerstag, 16.5.24, 14:15-15:15, Hörsaal II, Albertstr. 23b
Physical Control of Soft Robots
Montag, 27.5.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In this lecture I show that when multiple nonlinear soft actuators are interconnected they can also embody the control function, by leveraging the local negative stiffness of the actuators to drive their motion out of phase. This allows soft robots to move in pre-programmed sequence using only a single input.
Quantization of momentum maps and adapted formality morphisms
Montag, 27.5.24, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
If a Lie group acts on a Poisson manifold by Hamiltonian symmetries there is a well-understood way to get rid of unnecessary degrees of freedom and pass to a Poisson manifold of a lower dimension. This procedure is known as Poisson-Hamiltonian reduction. There is a similar construction for invariant star products admitting a quantum momentum map, which leads to a deformation quantization of the Poisson-Hamiltonian reduction of the classical limit. \n\nThe existence of quantum momentum maps is only known in very few cases, like linear Poisson structures and symplectic manifolds. The aim of this talk is to fill this gap and show that there is a universal way to find quantized momentum maps using so-called adapted formality morphisms which exist, if one considers nice enough Lie group actions. This is a joint work with Chiara Esposito, Ryszard Nest and Boris Tsygan.
Stationarity in beautiful pairs
Dienstag, 28.5.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
A type in a stable theory \(T\) is stationary if it has a unique non-forking extension. By adding imaginary elements to a model of \(T\), types over algebraically closed sets in the expanded structure become stationary. If \(T\) does not eliminate imaginaries, the question arises whether types over algebraically closed subsets in the original model (real subsets) are also stationary.\n\nAfter reviewing all the above notions, we will discuss this problem for the theory \(T_P\) of beautiful pairs of models of a stable theory \(T\) introduced by Poizat. By a result of Pillay and Vassiliev, this theory does not have (geometric) elimination of imaginaries if an infinite group is definable in \(T\). We will prove that types over real algebraically closed sets in \(T_P\) are stationary.
Periods via Motives and Species
Freitag, 31.5.24, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
We explain how the structure theory of finite dimensional algebras can be used to deduce dimension formulas for period spaces of motives. They are sharp and unconditional in the case of 1-motives, i.e., periods of curves. (Joint work with Martin Kalck, Graz)
Koszul duality
Montag, 3.6.24, 15:15-16:15, Raum 218, Ernst-Zermelo-Str. 1
I discuss how to reformulate local Langlands for real groups as an equivalence of categories and check some examples. \nIn the first lecture, I will discuss Koszul selfduality \nfor category O and the general formalism of Koszul duality.
On local boundary conditions for Dirac-type operators
Montag, 3.6.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
We give an overview on smooth local boundary conditions for Dirac-type operators, giving existence and non-existence results for local symmetric boundary conditions. We also \n discuss conditions when the boundary conditions are elliptic/regular/Shapiro-Lopatinski (i.e. in particular giving rise to self-adjoint Dirac operators with domain in \(H^1\)). This is joint work with Hanne van den Bosch (Universidad de Chile) and Alejandro Uribe (University of Michigan).
Friedman's and other Reflection Properties
Dienstag, 4.6.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
In 1975, Friedman introduced the property \(F(\bkappa)\),\nstating that every subset of \(\bkappa\) either contains or is disjoint\nfrom a closed set of ordertype \(\bomega_1\). Famously, this property\nfollows from the power forcing axiom ``Martin's Maximum''. In this\ntalk, we introduce posets which force the negation of this property and\nother related notions and investigate the patterns in which these\nproperties can fail in connection to large cardinals.
Wann regen Aufgaben Schülerinnen und Schüler zum «Mathematik betreiben» an?
Dienstag, 4.6.24, 18:30-19:30, Hörsaal II, Albertstr. 23b
Im Mathematikunterricht ist das Bearbeiten von Aufgaben eine zentrale Unterrichtstätigkeit. Wann regen diese Aufgaben dazu an, dass Mathematik betrieben wird und nicht nur Fertigkeiten trainiert werden? An erprobten Aufgaben aus verschiedenen mathematischen Kontexten der Sekundarstufe1 wird überlegt, wann im Unterrichtsprozess und mit welchen Aufgaben Lernende vielfältig mathematisch tätig sind.
Donnerstag, 6.6.24, 15:00-16:00, Hörsaal II, Albertstr. 23b
Koszul duality methods 2: Equivariant derived category and applications
Montag, 10.6.24, 15:15-16:15, Raum 218, Ernst-Zermelo-Str. 1
Ricci curvature, metric measure spaces and the Riemannian curvature-dimension condition
Montag, 10.6.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
I explain idea of synthetic Ricci curvature bounds for metric measure spaces and one of their applications in Riemannian geometry.
Phase separation on varying surfaces and convergence of diffuse interface approximations
Dienstag, 11.6.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
This talk's topic are phase separations on varying generalized hypersurfaces in\nEuclidian space. We consider a diffuse surface area (line tension) energy of Modica–\nMortola on surfaces and prove a compactness and lower bound estimate in the sharp interface\nlimit. We also consider an application to phase separated biomembranes where a Willmore energy\nfor the membranes is combined with a generalized line tension energy. For a diffuse\ndescription of such energies we give a lower bound estimate in the sharp interface limit. Time permitting I will present recent results about simultaneous phase field approximations of both the biomembrane and the indicator function for one of the two phases defined on the membrane.\n
Developments in Namba Forcing
Dienstag, 11.6.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
One way to study the properties of the infinite cardinals is to examine the extent to which they can be changed by forcing. In 1969 and 1970, Bukovsk{\b'y} and Namba independently showed that \(\baleph_2\) can be forced to be an ordinal of cofinality \(\baleph_0\) without collapsing \(\baleph_1\). The forcings they used and their variants are now known as Namba forcing. Shelah proved that Namba forcing collapses \(\baleph_3\) to an ordinal of cardinality \(\baleph_1\). In a 1990 paper, Bukovsky and Coplakova asked whether there can be an extension that collapses \(\baleph_2\) to an ordinal of cardinality \(\baleph_1\) without collapsing \(\baleph_3\). We will show that a slight strengthening of local precipitousness on \(\baleph_2\) due to Laver allows us to construct such an extension.\n
Analysis of Correlated Many-Body Systems: Bose-Einstein Condensates and Mean Field Spin Glasses
Donnerstag, 13.6.24, 08:30-09:30, Raum 404, Ernst-Zermelo-Str. 1
In this talk, I provide an overview of my recent research on the mathematical analysis of correlated many-body systems. I describe exemplary results concerning dilute quantum systems of interacting bosons and concerning disordered mean field systems of interacting Ising spins. In both cases, I carefully introduce the model, review relevant results and outline current as well as future research directions. The talk is based on joint work with M. Brooks, C. Caraci, J. Oldenburg, A. Schertzer, C. Xu and H.-T. Yau. .
Stabilization by transport noise and enhanced dissipation in the Kraichnan model
Donnerstag, 13.6.24, 10:40-11:40, Raum 404, Ernst-Zermelo-Str. 1
Thanks to the work of Arnold, Crauel, and Wihstutz it is known that for any self-\nadjoint operator T acting on a finite dimensional space with the negative trace the\ncorresponding linear equation dxt = T xt dt can be stabilized by a noise, i.e. there\nexists operator-valued Brownian motion W such that the solution of dxt + dW xt =\nT xt dt vanishes a.s. for any initial value x0 = x. The goal of the talk is to extend this\ntheorem to infinite dimensions. Namely, we prove that the equation dut = ∆ut dt\ncan be noise stabilized and that an arbitrary large exponential rate of decay can\nbe reached. The sufficient conditions on the noise are shown to be satisfied by the\nso-called Kraichnan model for stochastic transport of passive scalars in turbulent\nfluids. This talk is based on joint work with Prof. Benjamin Gess (MPI MiS and\nBielefeld University).
Sub-Riemannian geometries and hypoelliptic diffusion processes
Donnerstag, 13.6.24, 14:00-15:00, Raum 404, Ernst-Zermelo-Str. 1
I will start with an overview on sub-Riemannian geometries, where motion is only possible along certain admissible trajectories, and hypoelliptic diffusion processes, which due to underlying constraints spread in different directions at different orders. Subsequently, I will present two projects where the analysis of stochastic processes on constrained systems has proven to be fruitful. Firstly, I will discuss how a stochastic process introduced jointly with Barilari, Boscain and Cannarsa on surfaces in three-dimensional contact sub-Riemannian manifolds can be used to classify singular points arising in that setting. Secondly, I will show how the study of a standard one-dimensional Brownian motion conditioned to have vanishing iterated time integrals of all orders, which can be rephrased as studying projected hypoelliptic diffusion loops, has led to a novel polynomial approximation for Brownian motion..
Singular PDEs: regularity and homogenization
Donnerstag, 13.6.24, 16:10-17:10, Raum 404, Ernst-Zermelo-Str. 1
I will mostly focus on the regularity theory and homogenization for elliptic equations with degenerate unbounded coefficients, both at the deterministic (mostly done with Mathias Schäffner) as well as stochastic level. While already interesting on its own, I will mention two areas of use for these: study of regularity of critical points for variational integrals as well as invariance principle for random walks in random environments. At the end, I will conclude with a short discussion of few result in quantitative stochastic homogenization..
A semigroup approach for stochastic quasilinear equations driven by rough noise
Freitag, 14.6.24, 08:00-09:00, Raum 404, Ernst-Zermelo-Str. 1
We consider stochastic quasilinear equations perturbed by nonlinear multiplicative noise. Ex-ploring semigroup methods and combining techniques from functional analysis with tools from rough path theory, we establish the pathwise well-posedness of such equations. We apply our results to the stochastic Shigesada-Kawasaki-Teramoto equation describing population segregation by induced cross-diffusion and to the Landau-Lifshitz-Gilbert equation which models the magnetization of a ferromagnetic material. Moreover, we emphasize the advantage of rough path theory in the study of the long-time behavior of such systems. This talk is based on joint works with Antoine Hocquet and Christian Kuehn.
Optimal Transport and Diffusion on varying spaces
Freitag, 14.6.24, 10:10-11:10, Raum 404, Ernst-Zermelo-Str. 1
We discuss contraction estimates of diffusion under optimal transport problems on varying spaces. We further investigate in equivalent formulations and generalizations of these estimates.
From microscopic to macroscopic scales: effective evolution equations of many interacting particles.
Freitag, 14.6.24, 13:30-14:30, Raum 404, Ernst-Zermelo-Str. 1
Systems of interacting particles describing notable physical phenomena, such as time-irreversibility, Bose-Einstein condensation, superconductivity or superfluidity, represent a veritable challenge for mathematicians and physicists. They exhibit a daunting complexity, which renders the exact many-body theory non-approachable, not only from a mathematical viewpoint, but also for computer experiments and simulations. Therefore, an approximate description using effective macroscopic models is highly useful, and the rigorous study of the regime of validity of such approximations is of primary importance in mathematical physics. In this talk, I will present several settings leading to different effective kinetic equations and then I will focus on the mean-field regime for quantum particle systems, highlighting recent significant progress in the mathematical understanding of these systems.
Oscillatory effects in stochastic PDEs
Freitag, 14.6.24, 15:40-16:40, Raum 404, Ernst-Zermelo-Str. 1
I will describe two recent results related to the oscillations of the noise in stochastic PDEs. In the first example, a rougher-than-usual KPZ equation, the fluctuation of the noise is strong enough that on the relevant scale the nonlinearity turns into a new Gaussian noise via a central limit-type theorem. The second example, a 1-dimensional stochastic Allen Cahn equation, is much less singular and a solution theory is fairly unproblematic. Nevertheless, the averaging effects of the noise play a key role in their discretisations: they exhibit four times better temporal pointwise convergence rate than the pointwise regularity of the solution and twice better than the regularity of its single Fourier mode. Based on joint works with Ana Djurdjevac, Helena Kremp, Fabio Toninelli.
A necessary condition for zero modes of the Dirac equation
Montag, 17.6.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
We will state a necessary condition for the existence of a non-trivial solution of the Dirac equation, which is based on a Euclidean-Sobolev-type inequality. First, we will state the theorem in the flat setting and give an overview of the technical issues of the proof. Afterwards, we will consider and point out the main differences in the not necessarily flat setting. This talk is based on a work by R.Frank and M.Loss.
Existence of optimal flat ribbons
Dienstag, 18.6.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We revisit the classical problem of constructing a developable surface along a given Frenet curve \(\bgamma\) in space. First, we generalize a well-known formula, introduced in the literature by Sadowsky in 1930, for the Willmore energy of the rectifying developable of \(\bgamma\) to any (infinitely narrow) flat ribbon along the same curve. Then we apply the direct method of the calculus of variations to show the existence of a flat ribbon along \(\bgamma\) having minimal bending energy. Joint work with Simon Blatt.
Fredholmness of the Laplace operator on singular manifolds with pure Neumann Data
Montag, 24.6.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
Given a smooth Riemannian metric \(h\) on \(M\) one can consider the Laplace problem with pure Neumann data: Let \(\bDelta_h\) be the Laplacian given by \(h\) and \(n_h\) be the outer normal of \(\bpartial M\). Exists an \(u\) such that \((\bDelta_hu,\bpartial_{n_h}u)=(F,G)\) for some given data \(F\) and \(G\). There is no well posedness to this problem on singular mandifolds in regular Sobolev spaces but during the talk I will introduce a scale of weighted Sobolev spaces such that it is Fredholm. In the second part of the talk I will give a formula for the Fredholm Index depending on the chosen weight function.
Unipotent normal subgroups of algebraic groups
Dienstag, 25.6.24, 14:15-15:15, Hörsaal II, Albertstr. 23b
Der angewandte Mathematiker Henry Görtler vor und nach 1945.
Donnerstag, 27.6.24, 15:00-16:00, Hörsaal II, Albertstr. 23b
On finite generation of fundamental groups in algebraic geometry
Freitag, 28.6.24, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
The étale fundamental group of a (quasicompact) variety over complex numbers is (topologically) finitely presented by comparison with the topological case.\nIn characteristic p, the situation is much more subtle, as affine varieties have very large fundamental groups.\nBuilding on a recent breakthrough result by Esnault, Shusterman and Srinivas, I will explain how to extend the finite presentation statement to arbitrary proper varieties (joint work with Srinivas and Stix) and then (at least the finite generation part) to log/tame fundamental groups of schemes and rigid analytic spaces (joint work with Achinger, Hübner and Stix).\nThis requires revisiting the tame topology of rigid spaces and working with a certain class of non-fs log schemes.
Seminarvortrag zur Masterarbeit: „Normalformen in der Poisson-Geometrie“
Montag, 1.7.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
Gegeben ein Poisson-Hamilton-Raum mit hinreichend guter Gruppenwirkung lässt sich in einer Umgebung um die Impulsfläche der 0 mit einer Zusammenhangsform ein lokales Modell konstruieren, in welchem das System eine vereinfachte Gestalt annimmt.\n\nDafür werden wir den Rahmen der Poisson-Mannigfaltigkeiten verlassen und uns der Techniken einer Verallgemeinerung - den so genannten Dirac-Mannigfaltigkeiten - bedienen. Ich möchte diese im Rahmen des Vortrags diskutieren und schließlich die zentrale Idee des Beweises skizzieren.
Optimal control of rate-independent systems with non-convex energies
Dienstag, 2.7.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Rate-independent systems arise in multiple applications, in particular in computational mechanics. They model processes, which are invariant w.r.t. time transformations of external loads. In some applications such as perfect plasticity or brittle damage, the stored energy functional is not uniformly convex. In this case one cannot expect uniqueness and continuity (in time) of solutions. In particular due to the lack of continuity, a variety of solutions concepts has been developed in the recent past, among them global energetic solutions and parametrized balanced viscosity solutions. In the talk, we will consider optimal control problems governed by rate-independent systems with energy functionals that are not uniformly convex. The external loads will serve as control variables. Due to the lack of uniqueness of solutions, we regularize the state equation by adding viscosity. The main part of the talk will then be concerned with the viscosity limit, i.e., we will discuss, if, and under which conditions, solutions of the optimal control problems under consideration can be approximated via viscous regularization.
Zaubern mit Mathematik im Unterricht
Dienstag, 2.7.24, 18:30-19:30, Hörsaal II, Albertstr. 23b
Im Vortrag werden - zum Teil interaktiv - mathematische Zaubertricks vorgestellt, die spaß- und gewinnbringend an vielen Stellen im Unterricht in heterogenen Lerngruppen eingesetzt werden können. Es wird erläutert, wie etwa ein Zaubertrick zur mathematischen Sprachbildung beitragen kann, ein anderer funktionales Denken fördert.\n\nHäufig regen die Tricks zum Weiterfragen an. Dabei können einzelne Lernende oder Gruppen ihre je eigenen Fragestellungen entwickeln und verfolgen. Im Unterricht münden derartige Untersuchungen in neue „Zauber-Präsentationen“ und vertiefte Einblicke in mathematische\nZusammenhänge.\nLassen auch Sie sich verzaubern!
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Donnerstag, 4.7.24, 14:00-15:00, BBB
Sitzverteilungsverfahren
Donnerstag, 4.7.24, 15:00-16:00, Hörsaal II, Albertstr. 23b
Bei den Kommunalwahlen in Baden-Württemberg wird das Sainte-Laguë/Schepers-Verfahren angewandt, um das Wahlergebnis in eine Sitzverteilung an die Parteien umzurechnen. Mit diesem Verfahren soll das Verhältniswahlrecht möglichst gerecht ausgeführt werden.\n\n\nWie funktioniert das Verfahren? Gibt es schnellere Algorithmen als das Höchstzahlverfahren? In welchem Sinn sind die Regeln von Sainte-Laguë/Schepers optimal? Wir vergleichen mit anderen Divisor- und Proporzverfahren. \n
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Donnerstag, 4.7.24, 15:30-16:30, BBB
Abschlussfeier der Fakultät für Mathematik und Physik 2024
Freitag, 5.7.24, 14:30-15:30, Großer Hörsaal der Physik, Hermann-Herder-Str. 3 a
Sommerfest 2024
Freitag, 5.7.24, 15:30-16:30, Innenhof der Physik, Hermann-Herder-Str. 3 a
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Montag, 8.7.24, 09:00-10:00, BBB
Eine iterative Methode zur Lösung der Spin-Yamabe-Differentialgleichung
Montag, 8.7.24, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
Wir werden die partielle Spin-Yamabe-Differentialgleichung untersuchen, die sich aus einem Variationsproblem ergibt, das die klassische Yamabe-Gleichung auf den Kontext von Spin-Strukturen erweitert. Unser Schwerpunkt liegt auf der Lösung der Spin-Yamabe-Gleichung auf einer Mannigfaltigkeit mit Rand unter bestimmten Randbedingungen. Der Ansatz beinhaltet die iterative Lösung einer Folge von einfacheren PDEs, um eine konvergente Folge zu konstruieren, deren Grenzwert die Spin-Yamabe PDE löst. Zu den wichtigen Annahmen gehören eine sich gut verhaltene Randbedingung und die Anforderung, dass der erste Eigenwert des Dirac-Operators ausreichend groß ist, um Konvergenz zu gewährleisten.
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Dienstag, 9.7.24, 08:30-09:30, BBB
On the smooth classification of complete intersections
Donnerstag, 11.7.24, 00:00-01:00, Raum 318, Ernst-Zermelo-Str. 1
A complete intersection is a nonsingular complex projective variety\nformed as the intersection of a finite collection of hyper-surfaces. Regarded\nas oriented smooth manifolds, the classification of complete intersections is a\nclassical problem which has attracted the attention of many mathematicians. It\nis organised by the “Sullivan Conjecture”.\n\nIn this talk I will review the history and recent progress on this problem,\nreport on the verification of the Sullivan Conjecture in complex dimension 4 by\nmyself and Nagy, and discuss the outlook for future work in higher dimensions. \nThis is part of joint work with Nagy.\n
Global logarithmic deformation theory
Freitag, 12.7.24, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Global logarithmic deformation theory
Freitag, 12.7.24, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
A classical problem in algebraic geometry is the construction of smooth projective Calabi-Yau varieties, in particular of mirror pairs. In the approach via smoothings, the first step is to construct a reducible Gorenstein Calabi-Yau variety (or a pair thereof) by closed gluing of simple pieces. The second step is to find a family of Calabi-Yau varieties whose special fiber is the already constructed reducible Calabi-Yau variety, and whose general fiber is smooth. Logarithmic geometry, and especially logarithmic deformation theory, has given new impulses to the second step of this approach. In particular, the logarithmic version of the Bogomolov-Tian-Todorov theorem implies the existence of smoothings.\n\nIn this talk, we will see what logarithmic deformations are and by which types of Lie algebras they are controlled; we will discuss why logarithmic deformations are unobstructed in the Calabi-Yau case, and how their existence implies the existence of (non-logarithmic) smoothings.
Generative Models for the Design of Mechanical Metamaterials
Dienstag, 16.7.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
On some Fraïssé limits with free amalgamation
Dienstag, 16.7.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
I will present a general way of building some examples of NSOP1 theories as limit of some Fraïssé class satisfying strong conditions. We take interest in the properties of independence relations in these theories. In particular these limits will satisfy existence and we can compute Kim-forking and forking inside of them. These theories also come with a stationary independence relation. This study is based on results of Baudisch, Ramsey, Chernikov and Kruckman.
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Donnerstag, 18.7.24, 14:15-15:15, Raum 318, Ernst-Zermelo-Str. 1
On the smooth classification of complete intersections
Donnerstag, 18.7.24, 14:15-15:15, Raum 318, Ernst-Zermelo-Str. 1
A complete intersection is a nonsingular complex projective variety\nformed as the intersection of a finite collection of hyper-surfaces. Regarded\nas oriented smooth manifolds, the classification of complete intersections is a\nclassical problem which has attracted the attention of many mathematicians. It\nis organised by the “Sullivan Conjecture”.\n\nIn this talk I will review the history and recent progress on this problem,\nreport on the verification of the Sullivan Conjecture in complex dimension 4 by\nmyself and Nagy, and discuss the outlook for future work in higher dimensions. \nThis is part of joint work with Nagy.\n\n
Conformal deformation of a Riemannian metric via spinor field equations
Montag, 22.7.24, 16:00-17:00, Raum 127, Ernst-Zermelo-Str. 1
This talk is part of a program to establish the existence theory for the conformally invariant Dirac equation on a closed spin manifold. The study of such a nonlinear problem is motivated by its important applications in Spin geometry. Through the application of some new variational methods, our study aims to examine the behavior of solutions to the nonlinear Dirac equation and the primary goal is to obtain the existence of embedded spheres with prescribed mean curvature in Euclidean 3-space and to obtain a refined estimate for the Bär-Hijazi-Lott invariant.
Model-theoretic challenges in Constraint Satisfaction
Dienstag, 23.7.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Homogeneous structures and their reducts can be used to model many computational problems from finite model theory as constraint satisfaction problems (CSPs). In this talk I will give a survey on open model-theoretic problems for such structures that are relevant for obtaining complexity classification results for the corresponding CSPs. In particular, I will discuss finite homogeneous Ramsey expansions, reconstruction of structures up to bi-interpretability from the abstract automorphism group, and Thomas's conjecture about closed supergroups.\n\n
Vortragsreihe im Oberseminar: Alex Kaltenbach (TU Berlin) - A priori and a posteriori error identities for convex minimization problems based on convex duality relations
Mittwoch, 14.8.24, 14:00-15:00, (TBA)
A priori and a posteriori error identities for convex minimization problems based on convex duality relations\n\nA. Kaltenbach (TU Berlin)\n\nThe objective of this mini course is to develop a thorough error analysis for, in particular, non-smooth convex minimization problems on the basis of convex duality:\n\nAs a motivation example, we consider the celebrated Prager-Synge identity, the most famous example of an a posteriori error identity for the approximation of the Poisson problem. The original proof of the Prager-Synge identity resorts to Pythagoras' theorem, so that, initially, it seems like that the Prager-Synge identity cannot be generalized to non-linear or non-smooth problems. In this mini course, we will find that this is not true. More precisely, replacing Pythagoras' theorem by basic concepts from convex duality, we will find that the Prager-Synge identity can be generalized to a vast class of non-linear and non-smooth convex minimization problems.\n\nTo begin with, we recapitulate the most important concepts of convex duality theory: from basic notions from convex analysis via convex duality in the senses of Lagrange and Fenchel to the celebrated Fenchel duality theorem.\n\nThen, we apply the general Fenchel duality theory to a class of non-smooth convex minimization problems given through integral functionals and derive a generalized Prager-Synge identity, the so-called primal-dual gap identity.\n\nTo make the primal-dual gap identity practicable from a numerical point of view, using orthogonality relations between the Crouzeix-Raviart and the Raviart-Thomas elements, we transfer all convex duality relations to a discrete level.\n\nThe thus derived discrete convex duality relations, in turn, allow to derive an a posteriori error identity on a discrete level, which, eventually, turns out to be an a priori error identity.