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Thu, 21. Nov at 14:00
Smoothed analysis of the Simplex method: nearly tight noise dependence
Abstract. Smoothed analysis is a method for analysing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through worst-case analysis. Given an arbitrary linear program with $d$ variables and $n$ inequality constraints, we prove that there is a simplex method with smoothed complexity upper bounded by $O(\sigma^{-1/2} d^{11/4} \log(n/\sigma)^{7/4})$ pivot steps improving over the current best bound of $O(\sigma^{-3/2} d^{13/4} \log(n)^{7/4})$ pivot steps due to Huiberts, Lee and Zhang (STOC '23). For the same method we prove a lower bound on its smoothed complexity of $0.03 \sigma^{-1/2} d^{-1/4}\ln(n)^{-1/4}$ pivot steps for $n = (4/\sigma)^d$ inequality constraints. Here $\sigma > 0$ is the standard deviation of Gaussian distributed noise added to the original LP data. This nearly closes the gap between the upper and lower bounds in regards to their dependence on the noise parameter $\sigma$. In this talk we will discuss the algorithmic improvements that we used for the above new upper bound. This is joint work with Sophie Huiberts.
Thu, 21. Nov at 16:15
Arnimallee 3
Forcing Graphs and Graph Algebra Operators (Part II)
Abstract
Thu, 21. Nov at 16:15
TU Berlin, Instit...
Fluid limits of fragmented limit order markets
Abstract. Maglaras, Moallemi and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In this talk I will present the proof that, in the limit of small and frequent orders, the discrete system indeed converges to the fluid limit, which is characterized by a system of coupled nonlinear ODEs with singular coefficients at the origin. Moreover, I will discuss the temporal asymptotic stability for an arbitrary number of limit order books in that, over time, it converges to the stationary equilibrium state studied by Maglaras et al.
Thu, 21. Nov at 17:15
TU Berlin, Instit...
Optimal control of stochastic delay differential equations and applications to financial and economic models
Abstract. Optimal control problems involving Markovian stochastic differential equations have been extensively studied in the research literature; however, many real-world applications necessitate the consideration of path-dependent non-Markovian dynamics. In this talk, we consider an optimal control problem of (path-dependent) stochastic differential equations with delays in the state. To use the dynamic programming approach, we regain Markovianity by lifting the problem on a suitable Hilbert space. We characterize the value function $V$ of the problem as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, which is a fully non-linear second-order partial differential equation on a Hilbert space with an unbounded operator. Since no regularity results are available for viscosity solutions of these kinds of HJB equations, via a new finite-dimensional reduction procedure that allows us to use the regularity theory for finite-dimensional PDEs, we prove partial $C^{1,\alpha}$-regularity of $V$. When the diffusion is independent of the control, this regularity result allows us to define a candidate optimal feedback control. However, due to the lack of $C^2$-regularity of $V$, we cannot prove a verification theorem using standard techniques based on Ito’s formula. Thus, using a technical double approximation procedure, we construct functions approximating $V$, which are supersolutions of perturbed HJB equations and regular enough to satisfy a non-smooth Ito’s formula. This allows us to prove a verification theorem and construct optimal feedback controls. We provide applications to optimal advertising and portfolio optimization. We discuss how these results extend to the case of delays in the control variable (also) and discuss connections with new results of $C^{1,1}$-regularity of the value function and optimal synthesis for optimal control problems of stochastic differential equations on Hilbert spaces via viscosity solutions.
Tue, 26. Nov at 11:15
IRIS 1.207
Elliptic long-range quantum integrable systems
Abstract. There are at least two seemingly distinct realms of quantum integrability. The first domain is formed by the (short-range) Heisenberg spin chains, connected to the quantum inverse scattering method, which play a role in many different contexts both in physics and mathematics. The second domain is formed by the Calogero-Sutherland models and their deformations, which are families of differential or difference operators associated to root systems, with close ties to harmonic analysis, orthogonal Jack and Macdonald polynomials, and Knizhnik-Zamolodchikov equations. Their integrability follows from a connection to affine Hecke algebras. Understanding how these two realms are connected goes through the elliptic CS models and their generalisations, which are also interesting in their own right. I will discuss in what way this bridge between worlds is formed and how far we are in building it. Along the way I will try to point out connections to different research areas.
Tue, 26. Nov at 13:15
Room 3.006, Rudow...
Parahoric reduction theory of formal connections
Abstract. The celebrated reduction theory of formal connections is due to Hukuhara, Levelt, Turrittin, and Babbitt-Varadarajan, among others. In this talk, we will demonstrate the parahoric reduction theory of formal parahoric connections, which generalizes the aforementioned results and also extends Boalch’s result for the case of regular singularities. As applications, we will establish the equivalence between extrinsic and intrinsic definitions of regular singularities, as well as a parahoric version of Frenkel-Zhu’s Borel reduction theorem for formal connections. This is based on a recent joint work with Z. Hu, R. Sun, and R. Zong.
Tue, 26. Nov at 14:00
WIAS HVP5-7 R411 ...
Hybrid physics-informed neural network based dual-scale solver and its applications to learning-informed upscaling
Abstract. Inspired by the Liquid Composite Molding process for fiber-reinforced composites and its associated multiscale fluid flow structure, we present a novel framework for optimizing physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs), with applications to dual-scale PDE systems. Our hybrid approach approximates the fine-scale PDE using PINNs, producing a PDE residual-based objective subject to a coarse-scale PDE model parameterized by the fine-scale solution. Techniques from materials science introduce feedback mechanisms that yield scale-bridging coupling, resulting in a non-standard PDE-constrained optimization problem. From a discrete standpoint, the formulation represents a hybrid numerical solver that integrates both neural networks and finite elements. In this talk, we present the application setting, mathematical model, and highlights of its analysis, as well as outline perspectives on developing optimization algorithms for the hybrid framework in the infinite-dimensional setting.
Tue, 26. Nov at 18:00
FU Berlin,  Insti...
 Welt der Pseudogeraden
Abstract.  Wir erkunden zusammen die Welt der Pseudogeradenarrangements: Anordnungen von Kurven in der Ebene, von denen sich je zwei in genau einem Punkt kreuzen. Diese einfachen Objekte faszinieren mit ihren vielfältigen Bezügen zu verwandten Strukturen aus Kombinatorik, Geometrie und Informatik, wie zum Beispiel Sortiernetzwerke, Rhombenpflasterungen oder Young-Tableaux. Uns beschäftigt unter anderem die Frage, wie sich diese zufällig mithilfe einer Markov-Kette erzeugen lassen. Lassen sie sich einfach mischen wie ein Kartenstapel?
Wed, 27. Nov at 10:00
HVP 11 a, R.313
Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts
Fri, 29. Nov at 14:15
Urania
Undecidable problems in group theory
Wed, 04. Dec at 11:30
online
Can We Use Computers to Find Canonical Riemannian Metrics?
Abstract
Wed, 04. Dec at 14:15
WIAS, Erhard-Schm...
Discrete-to-continuum limit for reaction-diffusion systems via variational convergence of gradient systems
Abstract
Wed, 04. Dec at 16:00
Wed, 04. Dec at 16:00
Wed, 04. Dec at 16:30
EN 058
Positive Geometry in the plane
Abstract. I want to introduce positive geometries in the plane and discuss examples from discrete, convex, and algebraic geometry. There are open problems in this relatively simple case already and I will present one. This is mostly based on joint work with Kathlén Kohn, Ragni Piene, Kristian Ranestad, Felix Rydell, Boris Shapiro, Miruna-Stefana Sorea, and Simon Telen.
Thu, 05. Dec at 17:15
TU Berlin, Instit...
Wed, 11. Dec at 14:15
WIAS, Erhard-Schm...
What we know about square roots of elliptic systems -- and a bit more!
Abstract
Thu, 12. Dec at 14:00
Thu, 12. Dec at 16:00
BEL 301
Thesis defense
Abstract. Thesis defense Dante Luber
Fri, 13. Dec at 14:15
FU
Wed, 18. Dec at 11:30
online
Computational Aspects of Quadratic Forms in Determining the Representation Type of Quiver Algebras
Wed, 18. Dec at 16:00
Wed, 18. Dec at 16:00
Wed, 08. Jan at 14:15
WIAS, Erhard-Schm...
Thu, 09. Jan at 14:00
Fri, 10. Jan at 14:15
FU
Fri, 10. Jan at 14:15
FU
Wed, 15. Jan at 11:30
online
Data Transmission in Dynamical Random Networks
Abstract
Wed, 15. Jan at 11:30
online
Data Transmission in Dynamical Random Networks
Abstract
Tue, 21. Jan at 11:15
1.023 (BMS Room, ...
Wed, 22. Jan at 14:15
WIAS, Erhard-Schm...
Wed, 29. Jan at 11:30
online
Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
Abstract
Thu, 30. Jan at 17:15
TU Berlin, Instit...
Robust Portfolio Selection Under Recovery Average Value at Risk
Abstract. We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical Average Value at Risk shows that portfolio selection under its recovery version allows financial institutions to better control the recovery of liabilities while still allowing for tractable computations. The talk is based on joint work with Cosimo Munari, Justin PlĂĽckebaum and Lutz Wilhelmy.
Tue, 04. Feb at 11:15
1.023 (BMS Room, ...
Bi-Hamiltonian geometry of WDVV equations: general results
Abstract. It is known (work by Ferapontov and Mokhov) that a system of N-dimensional WDVV equations can be written as a pair of N-2 commuting quasilinear systems (first-order WDVV systems). In recent years, particular examples of such systems were shown to possess two compatible Hamiltonian operators, of the first and third order. It was also shown that all $3$-dimensional first-order WDVV systems possess such bi-Hamiltonian formalism. We prove that, for arbitrary N, if one first-order WDVV system has the above bi-Hamiltonian formalism, than all other commuting systems do. The proof needs some interesting results on the structure of the WDVV equations that will be discussed as well. (Joint work with S. Opanasenko).
Wed, 12. Feb at 11:30
online
Hybrid Models for Large Scale Infection Spread Simulations
Abstract
Wed, 12. Feb at 14:15
WIAS, Erhard-Schm...