* Seuraavan viikon tapahtumat merkitty tähdellä
Philine Schiewe (Aalto)
Integrating last-mile logistics and public transportation
* Monday 31 March 2025, 15:00, M2 (M233)
To handle the rising demand in last-mile deliveries without further straining the urban infrastructure, new delivery concepts have to be developed. We introduce a mathematical optimization model for two-echelon tour planning where the first echelon is operated by public transport vehicles and the the second echelon by small, potentially autonomous vehicles. We show that the capacity of the second-echelon vehicles as well as their number influence the complexity of the resulting problem and that even small instances cannot be solved by commercial integer programming solvers. However, we identify polynomially solvable special cases and thus develop fast heuristic solution approaches. A computational study along a bus line in Göttingen, Germany, shows that the developed heuristics can solve instances with up to 900 deliveries within minutes. At the same time, the delay imposed upon the bus line is insignificantly small.
SAL Seminar
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 1/4
* Tuesday 01 April 2025, 14:15, M3 (M234)
The first lecture of the course covers the topics:
1. Absolutely continuous functions on intervals - characterization and properties.
2. Beppo-Levi construction of Sobolev functions in Euclidean domains - weak derivatives, smooth approximations, ACLp -property.
3. Metric measure spaces and rectifiable curves; definition of path integrals.
4. p-Modulus of families of curves, and two lemmas of Fuglede.
Estibalitz Durand Cartagena (UNED, Madrid)
An introduction to metric spaces with small rough angles
* Wednesday 02 April 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 2/4
Friday 04 April 2025, 14:15, M3 (M234)
The second lecture of the course covers the topics:
5. Upper gradients and p-weak upper gradients; minimal ones in L^p-class.
6. Construction of Newton-Sobolev classes.
7. ACC_p-property and lattice property.
8. Banach space property of Newton-Sobolev classes, and substitute for reflexivity.
Yoh Tanimoto (University of Rome Tor Vergata)
Wightman and Osterwalder-Schrader axioms for two-dimensional CFT
Tuesday 08 April 2025, 10:15, M3 (M234)
We give an overview of various approaches to quantum field theory in general and an algebraic framework specific to two-dimensional CFT, (full) vertex operator algebras. One can define correlation functions in a full vertex algebra under some regularity conditions. We show that, under unitarity, they satisfy the Osterwalder-Schrader axioms. We sketch how the Wightman fields are recovered. (joint with Maria Stella Adamo, Luca Giorgetti and Yuto Moriwaki)
Prof. Dario Gasbarra (University of Vaasa) and Prof. Sangita Kulathinal (University of Helsinki)
Non-homogeneous multistate models for intermittently observed processes
Tuesday 08 April 2025, 15:15, M1 (M232)
Markov processes have a wide range of applications, and in many situations the underlying process is a non-homogeneous Markov (nhm) process. Here the transition probabilities and the initial distribution comprise the parameters. In scenarios where intermittent observations regarding the state occupancy are available, the observations provide only the partial information (the exact transition times are not observed) of the underlying process. In this talk, we will consider a 2-state nhm process {X(t), t ≥ 0} with the state space S = {1, 2}. When the process is observed only intermittently, the likelihood function is expressed in terms of the transition probabilities and numerical algorithms may be needed for the purpose of estimation. We will discuss a data augmentation approach based on Poisson processes for the estimation of the parameters. We will also describe characterisation of the transition intensities and extension of the proposed approach to two correlated processes. This work is motivated by the partial observations of treatment responses in patients of neovascular Age-related Macular Degeneration (nAMD). The characteristic feature of nAMD is the fluid accumulated under the macula due to leakage from abnormal blood vessels and the target of the treatment is to reduce the fluid.
Aleksis Koski
The internal Douglas condition
Wednesday 09 April 2025, 10:15, M3 (M234)
The Sobolev Jordan-Schoenflies problem asks a simple question: When does an embedding of the unit circle into the plane admit a homeomorphic extension in the Sobolev space W^1,p? Such a question is of basic interest in Nonlinear Elasticity, where Sobolev homeomorphisms describe an acceptable class of deformations between two elastic bodies. In a recent but important development, we have discovered an if and only if condition called the Internal Douglas Condition which gives a pleasingly complete answer to this problem in the planar case. In this talk, we will discuss this result and the related works leading up to it. This talk is based on joint work with Jani Onninen and Haiqing Xu.
Seminar on analysis and geometry
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 3/4
Wednesday 09 April 2025, 14:15, M2 (M233)
The third lecture of the course covers the topics:
9. Poincaré inequality - examples and connectedness property.
10. Poincaré inequality and doubling property of the measure - geometric consequences.
Hana Ephremidze (Universität Bonn)
TBA
Thursday 10 April 2025, 14:15, M2 (M233)
Algebra & Discrete Mathematics (ADM) Seminar
Prof. Iván Blanco Chacón (U. Alcalá)
A friendly invitation to Langlands's functoriality
Thursday 10 April 2025, 16:15, M3 (M234)
Elliptic curves and modular forms bring Galois representations (don't worry, these terms will be introduced/recalled in the talk). One of the many versions of Taylor-Wiles modularity theorem rephrases as: "representations attached to rational elliptic curves come from modular forms".
The power of this somewhat abstract statement is that it allows to prove Fermat's Last Theorem (with the aid of Ribet's level lowering theorem and Frey's curve, but that's other story).
In 2007, Dieulefait gave the first proof of the Serre modularity conjecture, generalising Taylor-Wiles, namely: Any rational Galois representation which "looks like" modular, is indeed modular. This statement was generalised in full by Khare and Wintenberger in 2011 (and that's also another story...)
Since then, a series of hits have established that any 2-dimensional "regular enough" Galois representation comes from modular-ish forms (namely, automorphic forms), so establishing a (conjectural) dictionary between arithmetic representations and automorphic ones. However, the following question remains openut (up to some minor results, includig the speaker's ones): to determine which group-theoretical representations preserve automorphicity.
The present talk is an introductory account of these ideas, a discussion of what's open and, time permitting, a statement of two of the works by the speaker.
ANTA Seminar / Hollanti et al.
Prof. Nageswari Shanmugalingam (University of Cincinnati)
Minicourse: Non-smooth analysis in metric spaces 4/4
Friday 11 April 2025, 14:15, M2 (M233)
The fourth lecture of the course covers the topics:
11. Poincaré inequality and doubling property of the measure - analytic consequences (density of Lipschitz functions, quasicontinuity).
12. Extreme cases: p=1 and p=\infty
This is also the last lecture of the mini course.
Jiasheng Lin (Institut de Mathématiques de Jussieu-Paris Rive Gauche)
Entanglement Entropy and Conical Singularities
Tuesday 15 April 2025, 10:15, M3 (M234)
In this talk we describe the work (arXiv:2501.19014) in collaboration with B. Estienne where we demonstrate a purely mathematical and geometric construction which recovers some results of Cardy and Calabrese on the so-called entanglement entropy. We start by explaining briefly the Segal picture of CFT (and QFT), and its natural relation to path-integral formulation. Then we introduce the entanglement entropy, and relate it to conical surfaces via path-integral and the "replica trick". Then we say briefly about geometry of conical singularities. Finally we formulate the main result of the work: we define CFT "partition functions" on surfaces with conical singularities, using a "Hadamard renormalization'' of the Polyakov anomaly integral. Then for a branched cover $f:\Sigma_d→\Sigma$ of degree $d$, the ratio $Z(\Sigma_d,f^*g)/Z(\Sigma,g)^d$ of partition functions transforms under conformal changes of g like a correlation function of CFT primary operators of specific conformal weights.
Anna-Mariya Otsetova (Midterm review)
TBA
Friday 25 April 2025, 11:15, M3 (M234)
Aapo Pulkkinen
TBA
Wednesday 07 May 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
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