Botond
Szabo
Bocconi Milan
Privacy constrained semiparametric inference
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16. October
Tomorrow
Learning to Compute Gröbner bases
Abstract.
Solving a polynomial system, or computing an associated \gb basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the worst case. In this talk, I present a new paradigm for addressing such problems, i.e., a machine-learning approach using a Transformer. The learning approach does not require an explicit algorithm design and can return the solutions in (roughly) constant time. This talk covers our initial results on this approach and relevant computational algebraic and machine learning challenges.
Janusz
Ginster
WIAS
Formation of microstructure for singularly perturbed problems related to helimagnets and shape-memory alloys
Abstract
Roan
Talbut
Imperial College
Tropical Gradient Descent
Abstract.
The field of tropical statistics - motivated by the identification of the tropical Grassmannian and the space of phylogenetic trees - has produced a range of unconstrained optimisation problems over the tropical projective torus. We will review the types of convexity exhibited by tropical loss functions in statistics, and we propose a new gradient descent method for solving tropical optimisation problems. Theoretical results establish global solvability for tropically star-quasi-convex problems, and numerical experiments demonstrate the method's superior performance over classical descent for tropical optimisation problems which exhibit tropical quasi-convexity but not classical convexity. Notably, tropical gradient descent seamlessly integrates into advanced optimisation methods, such as Adam, offering improved overall performance.
17. October
Thu W42
Stefan
Felsner
TU Berlin
On the number of arrangements of pseudolines: upper and lower bounds
21. October
Mon W43
Olexandr
Burylko
Institute of Mathematics, Kyiv, Ukraine
Reversible saddle-node separatrix-loop bifurcation
Rolf
Krause
Università della Svizzera italiana
Multilevel methods for non-smooth minimization and variational inequalities
22. October
Tue W43
A semismooth Newton method for obstacle-type quasivariational inequalities
Abstract.
Quasivariational inequalities (QVIs) are ubiquitous but, in particular, arise in PDE-constrained optimization in cases where the constraint set depends on the solution itself. In obstacle-type QVIs, this manifests as an obstacle that bends according to the state of the system. QVIs are notoriously hard to analyze, especially in the infinite-dimensional setting, and developing fast solvers posed in infinite dimensions has proven particularly challenging. As such most solvers in the literature rely on fixed point algorithms which can be slow to converge. In this talk, we introduce the first semismooth Newton method, posed in a Banach space setting, for such problems. We will see that the solver enjoys favourable properties such as local superlinear convergence and mesh independence.
23. October
Wed W43
Weining
Wang
University of Groningen
Conditional nonparametric variable screening by neural factor regression
Abstract.
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors or more generally a set of variables. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and a observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and two real world applications.
Arno
Siri-Jegousse
UNAM
Evgeny
Feigin
Tel Aviv University
Generalized chain polytopes, Grassmannians and representations
Abstract.
For a finite poset P we introduce a two-parameter family X(m,M) of polytopes defined by the set of inequalities labeled by subposets of P. The polytopes enjoy Minkowski sum property and are important for geometric and algebraic applications. We will discuss the connection of X(m,M) with the geometry of the classical Grassmann varieties. We will also construct a family of representations of the degenerate sl(n) Lie algebra admitting monomial bases labeled by integer points of X(m,M) (for the Grassmann poset P). The talk is based on https://arxiv.org/abs/2403.10074 (joint with Wojciech Samotij).
24. October
Thu W43
Matthew
Dupraz
Ronald
de Wolf
QuSoft, CWI and University of Amsterdam
Quantum Algorithms for Optimization
Abstract.
Faster algorithms for optimization problems are among the main potential applications for future quantum computers. There has been interesting progress in this area in recent years, for instance improved quantum algorithms for gradient descent and for solving linear and semidefinite programs. In this talk I will survey what we know about quantum speed-ups both for discrete and for continuous optimization, with a bit more detail about two speed-ups I worked on recently: for regularized linear regression and for Principal Component Analysis. I'll also discuss some issues with this line of work, in particular that quadratic or subquadratic quantum speed-ups will only kick in for very large instance sizes and that many of these algorithms require some kind of quantum RAM.
25. October
Fri W43
Bernd
Sturmfels
MPI-MiS Leipzig
The Two Lives of the Grassmannian
Abstract.
The Grassmannian parametrizes linear subspaces of a real vector space. It is both a projective variety (via Plücker coordinates) and an affine variety (via orthogonal projections). We examine these two representations, through the lenses of linear algebra, commutative algebra, and statistics.
29. October
Tue W44
Bernadette
Lessel
Bonn Universität
On the early history of quantum gravity
Abstract.
Quantum gravity, in the sense of a formal quantization of general relativity, had a first beginning in the year 1930. That year, the Belgian physicist Léon Rosenfeld published a seminal paper called "Zur Quantelung der Wellenfelder" in which he developed Heisenberg and Pauli's recently constructed method to quantize the electromagnetic field in order to apply it to the tetrad formulation of general relativity. In my talk, I aim to shed light on a perhaps surprising crucial historical influence that made this piece of intellectual work possible: that of unified field theory. A purely classical program, most prominently pursued by Albert Einstein and Hermann Weyl, to formally reduce the (classical) electromagnetic field to the gravitational field as described by general relativity.
30. October
Wed W44
Olga
Klopp
ESSEC Business School, Paris
Tomáš
Roubíček
Charles University Prague and Inst. of Thermomechanics, Czech Acad. Sci.
Time discretization in visco-elastodynamics at large displacements and strains in the Eulerian frame
Abstract
Rainer
Sinn
Leipzig University
31. October
Thu W44
Sebastian
Meyer
01. November
Fri W44
Heather
Harrington
MPI Dresden
Topology Data Analysis for Multiscale Biology
05. November
Tue W45
Guilherme
Feitosa de Almeida
Hannover Universität
1D Landau-Ginzburg superpotential of big quantum cohomology of CP2
Abstract.
Using the inverse period map of the Gauss-Manin connection associated with QH∗(CP2) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of CP2. In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the j-invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of QH∗(CP2) in closed form as the composition of the Weierstrass ℘-function and the universal coverings of C \ (Z ⊕ jZ) and C \ (Z ⊕ zZ) respectively. This seminar is based on the results of arXiv/2402.09574.
06. November
Wed W45
Computing Multiple Solutions of Topology Optimization Problems
David
Hobson
U of Warwick
Anna
Zamojska-Dzienio
Warsaw University of Technology
07. November
Thu W45
Alex
Black
David
Hobson
University of Warwick
Johannes
Muhle-Karbe
Imperial College London
12. November
Tue W46
Gernot
Akemann
Bielefeld Universität
Universality classes in non-Hermitian random matrices
13. November
Wed W46
14. November
Thu W46
Enrico
Bortoletto
and
Berenike
Masing
15. November
Fri W46
Ana Maria
Botero
U Bielefeld
and
José Ignacio
Burgos Gil
ICMAT
and
Jean-Benoît
Bost
U Paris XI
and
Maryna
Viazovska
EPFL
A Day of Arithmetic Geometry (on the occasion of the retirement of Jürg Kramer)
19. November
Tue W47
Certified Reduced-Order Methods for Model Predictive Control of Time-Varying Evolution Processes
Abstract.
In this talk model predictive control (MPC) is utilized to stabilize a class of linear time-varying parabolic partial differential equations (PDEs). In our first example the control input is only finite-dimensional, i.e., it enters as a time-depending linear combination of finitely many indicator functions whose total supports cover only a small part of the spatial domain. In the second example the PDE involve switching coefficient functions. We discuss stabilizability and the application of reduced-order models to derive algorithms with closed-loop guarantees. <p>This is joint work with , and Benjamin Unger (Stuttgart).</p>
Guillaume
Baverez
Aix-Marseille Université
Uniqueness of Malliavin-Kontsevich-Suhov measures
Abstract.
About 20 years ago, Kontsevich & Suhov conjectured the existence and uniqueness of a family of measures on the set of Jordan curves, characterised by conformal invariance and another property called 'conformal restriction'. This conjecture was motivated by (seemingly unrelated) works of Schramm, Lawler & Werner on stochastic Loewner evolutions (SLE), and Malliavin, Airault & Thalmaier on 'unitarising measures'. The existence of this family was settled by works of Werner-Kemppainen and Zhan, using a loop version of SLE. The uniqueness was recently obtained in a joint work with Jego. I will start by reviewing the different notions involved before giving some ideas of our proof of uniqueness: in a nutshell, we construct a family of 'orthogonal polynomials' which completely characterise the measure. In the remaining time, I will discuss the broader context in which our construction fits, namely the conformal field theory associated with SLE.
20. November
Wed W47
Bernhard
Stankewitz
Universität Potsdam
Martin
Winter
Dirichlet Postdoc
Of Rigid and Flexible Polytopes
Julia
Komjathy
TU Delft
21. November
Thu W47
Eleonore
Bach
Yonatan
Shadmi
Imperial College London
27. November
Wed W48
Julien
Chhor
Toulouse School of Economics
04. December
Wed W49
Fabian
Lehmann
Dirichlet Postdoc
Calabi-Yau 3-Folds with Boundary
Patrick
Cheridito
ETH Zurich
Günter
Last
KIT
05. December
Thu W49
Patrick
Cheridito
ETH Zürich
11. December
Wed W50
Sebastian
Bechtel
Université Paris-Saclay, France
12. December
Thu W50
Hana
Kourimska
Dante
Luber
Thesis defense
Abstract.
Thesis defense Dante Luber
13. December
Fri W50
Roman
Sauer
KIT
18. December
Wed W51
Jan Marten
Sevenster
Computational Aspects of Quadratic Forms in Determining the Representation Type of Quiver Algebras
Zhen-Qing
Chen
U of Washington
09. January
Thu W01
Roxana
Radulescu
10. January
Fri W01
Ilya
Cheyrev
U Edinburgh
15. January
Wed W02
21. January
Tue W03
Olivier
Marchal
Univ. St-Etienne
29. January
Wed W04
Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
Abstract
30. January
Thu W04
Stefan
Weber
Leibniz Universität Hannover
12. February
Wed W06