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Padova Seminars in Probability and Finance - Domenico Marinucci - 14:30, May 17th
by Alberto Chiarini 13 May '24

13 May '24

Dear all, It is our pleasure to invite you all to the Padova Seminars in Probability and Finance on May, 17th at 14:30, at the department of Mathematics in Padova for the seminar by: Domenico Marinucci (University of Rome "Tor Vergata") Title: Geometry and Topology of Spin Random Fields Date: May 17, 2024, at 14:30, 2AB45 Abstract: Spin random fields are very important in many physical applications; they can be viewed as random sections of the s-th complex tensor power of the tangent bundle of the 2-sphere. In this talk, we discuss how to characterize their expected geometry and topology. In particular, we investigate the asymptotic behaviour, under scaling assumptions, of general classes of geometric and topological functionals for (properly defined) excursion sets; we cover both the cases of fixed and diverging spin parameters s. In the special case of monochromatic fields (i.e., spin random eigenfunctions), we show how their asymptotic behaviour is non-universal; we can obtain complex versions of Berry's random waves and of Bargmann-Fock's model as subcases of a new general class, depending on the rate of divergence of the spin parameter. We shall also discuss how these random fields can be reparametrised into complex-valued random functions on the group of rotations SO(3), and we discuss the expected values of the same geometric functionals in this new framework. Based on joint works with Javier Carròn Duque, Antonio Lerario, Maurizia Rossi and Michele Stecconi. Best wishes, Alberto and Alekos

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SPASS Seminar: Yassine Tahraoui
by Francesco Grotto 13 May '24

13 May '24

Dear Colleagues, We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi: *Stochastic obstacle problems: variational & non variational settings* by Yassine Tahraoui (Scuola Normale Superiore) The seminar will take place tomorrow TUE, 14.05.2024 at 14:00 CET in Aula Seminari, Dipartimento di Matematica, UNIPI and streamed online at the link below. The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass *---------------------------------------------------------* *Abstract: Obstacle problems are free boundary type problems, well known in the literature of applied mathematics and lead to numerous applications. My aim is to present some results about the well-posedness and the regularity of the solution to a "parabolic or hyperbolic" obstacle problem in the presence of multiplicative noise, studied in [1, 2]. After showing the well-posedness of such problems, we prove Lewy-Stampacchia's inequalities, which gives an estimate of the reflected measure generated by the singularities caused by the obstacle near the free boundary.* *[1]I. H. Biswas, Y. Tahraoui and G. Vallet: Obstacle problem for a stochastic conservation law and Lewy-Stampacchia inequality. Journal of Mathematical Analysis and Applications, 527 (1) 127356 (2023)* *[2]Y. Tahraoui and G.Vallet: Lewy-Stampacchia's inequality for a stochastic T-monotone obstacle problem. Stochastic Partial Differential Equations: Analysis and Computations 10, 90-125 (2022).*

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Seminar in Statistics - ALEX MUNK
by Pierpaolo De Blasi 13 May '24

13 May '24

SEMINARS IN STATISTICS @ COLLEGIO CARLO ALBERTO <https://www.carloalberto.org/events/category/seminars/seminars-in-statistic…> Venerdi 17 Maggio 2024, alle ore 12.00, presso il Collegio Carlo Alberto, in Piazza Arbarello 8, Torino, si terrà il seguente seminario: ------------------------------------------------ Speaker: Alex Munk (Georg August Universitat Gottingen) Title: *Optimal Transport Dependency* Abstract: Finding meaningful ways to determine the dependency between two random variables 𝜉 and 𝜁 is a timeless statistical endeavor with vast practical relevance. In recent years, several concepts that aim to extend classical means (such as the Pearson correlation or rank-based coefficients like Spearman’s 𝜌) to more general spaces have been introduced and popularized, a well-known example being the distance correlation. In this talk, we propose and study an alternative framework for measuring statistical dependency, the transport dependency 𝜏 ≥ 0 (TD), which relies on the notion of optimal transport and is applicable in general Polish spaces. It can be estimated via the corresponding empirical measure, is versatile and adaptable to various scenarios by proper choices of the cost function. It intrinsically respects metric and geometric properties of the ground spaces. Notably, statistical independence is characterized by 𝜏 = 0, while large values of 𝜏 indicate highly regular relations between 𝜉 and 𝜁 . Based on sharp upper bounds, we exploit three distinct dependency coefficients with values in [0, 1], each of which emphasizes different functional relations: These transport correlations attain the value 1 if and only if 𝜁 = 𝜑(𝜉), where 𝜑 is a) a Lipschitz function, b) a measurable function, c) a multiple of an isometry. Besides a conceptual discussion of transport dependency, we address numerical issues and its ability to adapt automatically to the potentially low intrinsic dimension of the ground space. Monte Carlo results suggest that TD is a robust quantity that efficiently discerns dependency structure from noise for data sets with complex internal metric geometry. The use of TD for inferential tasks is illustrated for independence testing on a data set of trees from cancer genetics. Joint work with Giacomo Nies and Thomas Staudt. ------------------------------------------------ Sarà possibile seguire il seminario anche in streaming: Join Zoom Meeting <https://us02web.zoom.us/j/81354066852?pwd=a2hEZTFHMDRuZHVYQ1RGSmd0Wi82QT09> Il seminario è organizzato dalla "de Castro" Statistics Initiative www.carloalberto.org/stats -- Pierpaolo De Blasi University of Torino & Collegio Carlo Alberto carloalberto.org/pdeblasi <https://sites.google.com/a/carloalberto.org/pdeblasi/>

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Seminario Karel Hron presso Politecnico di Milano
by Laura Maria Sangalli 12 May '24

12 May '24

Si avvisa che in data 15-05-2024, alle ore 11:00 precise al Politecnico di Milano, in aula Saleri (sesto piano Dipartimento di Matematica - edificio 14), si svolgerà il seguente seminario Karel Hron, University Olomouc Titolo: Analysing multivariate densities in Bayes spaces with implications for functional data analysis Abstract: Probability density functions can be embedded in the geometric framework of Bayes spaces which respect their relative nature and enable further modeling and analysis. Specifically, the Hilbert space structure of Bayes spaces (whereof compositional data are one specific instance) has several important implications for classical and Bayesian inference, as well as functional data analysis. In this contribution, an orthogonal decomposition of multivariate densities in Bayes spaces using a distributional analog of the Hoeffding-Sobol identity is constructed. The decomposition is based on a reformulation of the standard (arithmetic) margins into so-called geometric margins. These are orthogonal projections into one-dimensional space of information contained in multivariate densities and coincide with the arithmetic margins in case of independence. More generally, the decomposition contains an independent part and all possible interaction terms. The orthogonality of the decomposition results in an analog of Pythagoras' Theorem for squared norms of the decomposed densities and margin-free property of the interaction terms. Because the squared norms from the Pythagoras' decomposition are essentially compositional in nature, all tools of the log-ratio methodology can be used for their statistical processing. Theoretical results will be illustrated with empirical geochemical data. This talk is based on joint work with Christian Genest and Johanna Nešlehová from McGill University, Montréal, Canada. Il link per seguire il seminario online sarà reso disponibile pochi minuti prima dell’avvio del seminario al seguente link https://mox.polimi.it/mox-colloquia-seminars-list/mox-seminars/?id_evento=2… Tutti gli interessati sono cordialmente invitati a partecipare, Laura Sangalli —— Laura Maria Sangalli MOX - Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci 32 20133 Milano - Italy (+39) 02 2399 4554 laura.sangalli(a)polimi.it<mailto:laura.sangalli@polimi.it> https://sangalli.faculty.polimi.it

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International Conference in Venice - CALL FOR PAPERS
by Monica Billio 12 May '24

12 May '24

23nd INTERNATIONAL CONFERENCE CREDIT 2024 *The frontiers of new risks: AI, digital and sustainability transitions * Venice, Italy 3 – 4 October 2024 * * *GRETA Associati* (Venice, Italy),*CRIF* (Bologna, Italy), *European Datawarehouse *(Frankfurt am Main, Germany), *European Investment Fund* (Luxembourg), *Intesa Sanpaolo* (Milan, Italy) and *Modefinance* (Trieste, Italy) are partners in organising a Conference to be held in Venice on October 3-4, 2024. * * The CREDIT 2024 conference will bring together academics, practitioners and PhD students working in various areas of financial and socio-economic risk with the aim of creating a unique opportunity for participants to discuss research progress and policy as well as industry-relevant insights and directions for future research. CREDIT 2024 is the *twenty-third* in a series of events dedicated to various aspects of credit risk and organised under the auspices of: the *Department of Economics *and*VERA - Venice centre in Economic and Risk Analytics for public policies* - of the *Ca’ Foscari University of Venice*,*Joint Research Center European Commission*, *ABI - Italian Banking Association*, *AIAF - Associazione Italiana per l'Analisi Finanziaria*, *AIFIRM - Associazione Italiana Financial Industry Risk Managers*. Sustainability necessarily involves the adaptation of today’s business model to the dynamic nature of the current digitalised environments. Corporations need to make sure that resources, especially technology, are being used responsibly and efficiently to improve the lives of the present generations and future generations as well as strengthen their relationships with the environment as to solve sustainability-related problems such as poverty, environmental degradation, pollution and inequality. Artificial Intelligence (AI) has the potential to address these societal problems including sustainability. The climate crisis and the degradation of the physical environment are complex problems that require the most innovative and advanced solutions. The real value of AI hence lies in its ability to facilitate and foster environmental and social governance, rather just as a tool to reduce pollution, poverty and resource depletion. In the age of AI, societies depend on big data, social media, knowledge management and data science to survive and achieve these sustainability goals. AI has the potential to reshape not only finance and industry but also the whole society. There is need to understand opportunities and challenges as to properly manage all relevant risks. The organisers encourage submissions on any topic within the overall theme of the conference, with attention to *the use of AI to assess the sustainability impact of finance *(i.e. exploiting AI techniques or Big Data to bridge primary information gaps and proxy the sustainability impact) and *on how climate and digital risks may interact* (i.e. climate denial, social media and social media strategies including deepfakes). The final program will include both submitted and invited papers. Acceptances received so far from invited speakers include *Patrick Bolton *(Imperial College London), and *Roberto Rigobon* (MIT Sloan School of Management). The Conference will also include panel discussions on the major issues at stake with the views of researchers', practitioners' and policy makers. The SCIENTIFIC COMMITTEE for the Conference consists of: *Marcin Kacperczyk *(Imperial College London, Programme Chair) *Monica Billio* (Ca’ Foscari University of Venice & GRETA) *Marie Brière* (AMUNDI & Université Libre de Bruxelles) *Lucia Alessi* (Joint Research Center, European Commission) *Leonardo Gambacorta *(Bank For International Settlements) *Mila Getmansky* (Isenberg School of Management, UMass Amherst) *Christian Gollier* (Toulouse School of Economics) *Helmut Kraemer-Eis *(European Investment Fund) *Jan Pieter Krahnen *(Leibniz Institute for Financial Research SAFE & Goethe University) *Steven Ongena* (University of Zurich, Swiss Finance Institute, KU Leuven, NTNU Business School & CEPR) *Roberto Rigobon *(MIT Sloan School of Management) *Stephen Schaefer* (London Business School) *Marti Subrahmanyam *(NYU Stern Business School) CALL FOR PAPERS Those wishing to present a paper at the Conference should submit by *June 10, 2024 *to the address given below (preferably in electronic format). Please indicate to whom correspondence should be addressed. Decisions regarding acceptance will be made by July 10, 2024. The final version of accepted papers must be received by August 31, 2024. Please send papers to: GRETA Associati, Dorsoduro 3707 - 30123 Venice, ITALY Phone : +39 349 060 3656 - e-mail: credit(a)greta.it More detailed information on the Conference website: https://www.greta.it/index.php/it/credit-2024

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Seminar RUSSO
by Stefano Pagliarani 10 May '24

10 May '24

Dear all, On May 15th, at 11 am, in the classroom Aula Seminari VIII Piano, Department of Mathematics of the University of Bologna, Francesco RUSSO will give a seminar entitled WEAK DIRICHLET PROCESSES AND BSDE<https://www.dm.unibo.it/seminari/mat/seminars/2024/05/15/francesco-russo>s The abstract is available at https://www.dm.unibo.it/seminari/mat/seminars/2024/05/15/francesco-russo For any question, please contact the organizers: Cristina di Girolami and Stefano Pagliarani. Best regards, ------------------------------------------------------------------------------------------------------------------------ Stefano Pagliarani, Associate Professor Piazza di Porta S. Donato, 5 University of Bologna (Alma Mater) 40126 Bologna (BO), Italy Department of Mathematics Cell. Phone +39 366 5013755 Email: stepagliara1(a)gmail.com<mailto:stepagliara1@gmail.com>, <mailto:stefano.pagliarani9@unibo.it> stefano.pagliarani9(a)unibo.it<mailto:stefano.pagliarani9@unibo.it> Zoom: https://unibo.zoom.us/j/3755841669 -----------------------------------------------------------------------------------------------------------------------

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Fwd: Summer School Ischia ESI
by Roy Cerqueti 09 May '24

09 May '24

Dear all, please, find the flyer of this Summer School, that can be of interest to some young scholars. Thank you. Yours sincerely, Roy Cerqueti -- *Fai crescere le giovani ricercatrici e i giovani ricercatori*** *con il 5 per mille alla Sapienza* Scrivi il codice fiscale dell'Università *80209930587 **Cinque per mille <https://www.uniroma1.it/it/node/23149>*

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Fwd: Next LTI@Unito Seminar: Stéphane Villeneuve | May 13 @ 12:00 - 13:00
by Luca Regis 08 May '24

08 May '24

Dear colleagues, please find below the announcement of the seminar by Stephane Villeneuve (TSE) organized by LTI@UniTO and Collegio Carlo Alberto. The seminar can be attended via zoom clicking on the button below. Best regards, Luca Regis ---------------------------------------- Associate Professor ESOMAS Department, University of Torino Affiliate, Collegio Carlo Alberto sites.google.com/view/lucaregis Office: +39 011 670 6065 www.carloalberto.org/lti Next LTI@Unito Seminar: Stéphane Villeneuve | May 13 @ 12:00 - 13:00 <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeFuBop7S3TtlKvKzHBSs/4oJ_v…> LTI@UniTO and Fondazione Collegio Carlo Alberto are pleased to invite you to the following seminar: *May 13, 2024 | 12:00 - 13:00* *Dynamic contracting with many agents* *Stéphane Villeneuve (Toulouse School of Economics)* *Abstract: *We analyze dynamic capital allocation and risk sharing between a principal and many agents, who privately observe their output. The state variables of the mechanism design problem are aggregate capital and the distribution of continuation utilities across agents. This gives rise to a Bellman equation in an infinite dimensional space, which we solve with mean-field techniques. We fully characterize the optimal mechanism and show that the level of risk agents must be exposed to for incentive reasons is decreasing in their initial outside utility. We extend classical welfare theorems by showing that any incentive-constrained optimal allocation can be implemented as an equilibrium allocation, with appropriate money issuance and wealth taxation by the principal. To attend online, join Zoom meeting <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeG13GxwPEe3FQkdjFU38/HGpf3…> *Fondazione Collegio Carlo Alberto* Piazza Arbarello 8 - 10122 Torino, Italy phone: +3901115630800 <tel:+3901115630800> segreteria(a)carloalberto.org - www.carloalberto.org <https://4z5y5.r.sp1-brevo.net/mk/mr/sh/SMJz09SDriOHWoY4zxneDRikeAJG/JT1digZ…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeG7uj6lMPoCjWZwTDmdO/xbd5a…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGEmBFaJayMDcPFDC5De/7R5hd…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGLddOPGm8VhiEXxANnu/KmFdZ…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGSV5XEDxIfBo3qh8gOA/THQZY…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGZMXg3B8Softt9R6yyQ/xDNI-…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGgDzos8Jcy9ziSB5HYg/jDbOw…> *Founders* <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGn5Rxh5Un7e5Xkv3a8w/r0Vb5…> <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/SMK1E8tHeGtwu6W2fxH8BN3f1sjC/phw27…> *Sostieni il Collegio Carlo Alberto con il 5x1000 | c.f. 94049090015* *INFORMATION UNDER THE NEW GENERAL DATA PROTECTION REGULATION (GDPR)* Your personal information has been gathered for the exclusive purpose of informing you about the Collegio's initiatives, considering our and your legitimate interest or your consent. If you wish to have your personal data modified please contact Fondazione Collegio Carlo Alberto, piazza Arbarello 8, 1022 Torino, Italy - phone:+39011 15630 800 - privacy(a)carloalberto.org <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/1t6Af4OiGsDhYHezxFlTns9XmrPqba/o-w…> To find out about the policies regarding the processing of personal data pursuant to articles 13-14 of EU Regulation 2016/679, consult the information at the following link _https://www.carloalberto.org/privacy/_ <https://4z5y5.r.sp1-brevo.net/mk/cl/f/sh/1t6Af4OiGsE9szrQLbrOy8DNAgOaJe/Drj…> *Unsubscribe* <https://4z5y5.r.sp1-brevo.net/mk/un/sh/SMJz09a0vkbXsu1klhxRMEbrtrvO/3tb3NOW…> *© 2022 Fondazione Collegio Carlo Alberto*

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STATISTICAL REFLECTIONS: Half-day Workshop on Statistical Methods - Ca’ Foscari University (Scientific Campus Venezia Mestre)
by Carlo Gaetan 08 May '24

08 May '24

Dear all, the STREAM group (https://www.unive.it/pag/16818/) of the Ca’ Foscari university invites to *STATISTICAL REFLECTIONS* *Half-day Workshop on Statistical Methods* *Venice May 22, 2024* Ca’ Foscari University Scientific Campus Aula Delta 1B Via Torino 155 Venezia Mestre Program: -14:00 David Firth (University of Warwick): Compositional quasi-likelihood and logit models -14:45 Ioannis Kosmidis (University of Warwick): Consistent, tuning-free model selection in regression problems -15:30 Omiros Papaspiliopoulos (Bocconi University): Functional estimation of the marginal likelihood Abstracts: Professor David Firth University of Warwick, UK https://warwick.ac.uk/dfirth Compositional quasi-likelihood and logit models A composition vector describes the relative sizes of parts of a thing. Some important modern application areas are microbiome analysis, time-use analysis and archaeometry (to name just three). We develop model-based analysis of composition, through the first two moments of measurements on their original scale. In current applied work the most-used route to compositional data analysis, following an approach introduced by the late John Aitchison in the 1980s, is based on contrasts among log-transformed measurements. The quasi-likelihood model framework developed here provides a general alternative with several advantages. These include robustness to secondary aspects of model specification, stability when there are zero-valued or near-zero measurements in the data, and more direct interpretation. Linear models for log-contrast transformed data are replaced by generalized linear models with logit link, and variance-covariance estimation is straightforward via suitably standardized residuals. Joint work with Fiona Sammut, University of Malta. Professor Ioannis Kosmidis University of Warwick, UK https://www.ikosmidis.com Consistent, tuning-free model selection in regression problems We present a family of consistent model selection procedures for regression problems, which appropriately threshold readily available statistics after estimating the model with all covariate information. The model selection procedures rely only on standard assumptions about information accumulation that guarantee the typically expected asymptotic properties of the estimators (e.g., consistency) and require neither the selection of tuning parameters nor the fitting of all possible models. We apply our thresholding methodology in widely used statistical models (e.g. generalized linear models and beta regression), demonstrate that it is easily implementable as part of the standard maximum likelihood output, and compare its performance to existing techniques, illustrating its effectiveness. Joint work with Patrick Zietkiewicz, University of Warwick. Professor Omiros Papaspiliopoulos Bocconi University, Italy https://dec.unibocconi.eu/people/omiros-papaspiliopoulos Functional estimation of the marginal likelihood We consider the problem of exploring the marginal likelihood of low-dimensional hyperparameters from high-dimensional Bayesian hierarchical models. We provide a unified framework that connects seemingly unconnected approaches to estimating normalizing constants, including the Vardi estimator, the umbrella sampling and the Gibbs sampler. The framework requires Monte Carlo sampling from the posteriors of the high-dimensional parameters for different values of the hyperparameters on a lattice. We establish a surprising reproducing property that leads to a functional estimator of the marginal likelihood and establish consistency both fixed-lattice and lattice-infill consistency. The resultant method is highly practical, black-box with theoretical guarantees. Best regards, Carlo Gaetan -- - Dipartimento di Scienze Ambientali, Informatica e Statistica - DAIS Università Ca' Foscari - Venezia Z.A12 - Edificio Zeta Via Torino, 155 I-30172 Mestre (VE) ITALY phone: ++39 041 234 8404 e-mail:[gaetan"at"unive"dot"it] web:[http://www.dais.unive.it/~gaetan] Please don't print this e-mail unless you really need to. Please avoid sending me Word, Excel or PowerPoint attachments. Seehttp://www.gnu.org/philosophy/no-word-attachments.html. Per favore non stampate questo messaggio se non è proprio necessario. Per favore non mandatemi allegati in Word, Excel o PowerPoint. Le ragioni sono spiegate quihttp://www.gnu.org/philosophy/no-word-attachments.it.html

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Kolmogorov meets Turing - May 23, 11am - 6pm, DIAG, Sapienza, Rome
by Marco Scarsini 07 May '24

07 May '24

Kolmogorov meets Turing *Workshop on probabilistic methods for the analysis of stochastic processes and randomized algorithms* This year's edition of the Kolmogorov meets Turing Workshop will take place on Thursday, May 23rd 2024, at DIAG <https://www.diag.uniroma1.it/>, via Ariosto 25, Aula Magna I floor. The purpose of KmT is to bring together researchers from Computer Science, Economics, Mathematics and related fields to present and discuss research on probabilistic methods for the analysis of games, distributed and stochastic processes, dynamic processes and randomized algorithms. When: Thursday May 23rd, 2024 Where: Dipartimento di Ingegneria Informatica, Automatica e Gestionale “A. Ruberti”, via Ariosto 25, Roma – Aula Magna, I floor Schedule Morning session 11.00 – 12.00. Nicolò Cesa-Bianchi (Università degli Studi di Milano): The mathematics of machine learning: between statistics and game theory 12.00 – 12.30. Xavier Mathieu Raymond Venel (Luiss University): Weighted average-convexity in Cooperative Games 12.30 – 13.00. Guido Schaefer (CWI, Netherlands): To Trust or Not to Trust: Assignment Mechanisms with Predictions 13.00 – 14.30: Lunch break Afternoon session 14.30 – 15.00. Pietro Caputo (University Roma Tre): Nonlinear Monte Carlo dynamics for the Ising model: some convergence results 15.00 – 15.30. Matteo Quattropani (Sapienza University of Rome): Mixing of the Averaging process on graphs and hypergraphs 15.30 – 16.00. Robin Vacus (Bocconi University): Minority Dynamics: the Short and Winding Road to Consensus 16.00 – 16.30: Coffee break 16.30 – 17.00. Maria Sofia Bucarelli (Sapienza University of Rome): On Generalization Bounds for Projective Clustering 17.00 – 17.30. Francesco D'Amore (Bocconi University): The Strong Lottery Ticket Hypothesis and the Random Subset Sum Problem 17.30 – 18.00. Federico Fusco (Sapienza University of Rome): The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations _______________________________________________________ LIST OF ABSTRACTS Maria Sofia Bucarelli: On Generalization Bounds for Projective Clustering. Given a set of points, clustering consists of finding a partition of a point set into k clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the famous k-median and k-means objectives. One may also choose centers to be j dimensional subspaces, which gives rise to subspace clustering. In this paper, we consider learning bounds for these problems. That is, given a set of n samples P drawn independently from some unknown, but fixed distribution D, how quickly does a solution computed on P converge to the optimal clustering of D? We give several near p optimal results. In particular, 1) For center-based objectives, we show a convergence rate of O(√k/n). This matches the known optimal bounds of [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] and [Bartlett, Linder, and Lugosi, IEEE Trans. Inf. Theory 1998] for k-means and extends it to other important objectives such as k-median. 2) For subspace clustering with j-dimensional subspaces, we show a convergence rate of O(√kj2/n). These are the first provable bounds for most of these problems. For the specific case of projective clustering, which generalizes k-means, we show a converge rate of Ω(√kj/n) is necessary, thereby proving that the bounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] are essentially optimal. Nicolò Cesa-Bianchi: The mathematics of machine learning: between statistics and game theory. Machine learning is the main driving force behind the current AI revolution. To provide a solid mathematical foundation to learning systems, we must formally characterize what a machine can learn and what is the minimal amount of training data needed to achieve a desired performance. In this talk, I will describe the two main approaches to algorithmic learnability, one rooted in statistics and one in game theory, and explore their connections. Pietro Caputo: Nonlinear Monte Carlo dynamics for the Ising model: some convergence results. We introduce and analyze a natural class of nonlinear Monte Carlo dynamics for spin systems such as the Ising model. The evolution is based on the framework of mass action kinetics, which models systems undergoing collisions, and captures a number of nonlinear models from various fields, including chemical reaction networks, Boltzmann’s model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a nonlinear analog of the familiar Monte Carlo method based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. The nonlinearity makes the dynamics much harder to analyze, and even the most basic convergence issues are far from being settled. We discuss several open problems. The main result is an optimal estimate on the rate of convergence to stationarity in a regime of high temperature. Our analysis combines tools from percolation, branching and fragmentation processes. Based on joint work with Alistair Sinclair. Francesco D’Amore: The Strong Lottery Ticket Hypothesis and the Random Subset Sum Problem. The Strong Lottery Ticket Hypothesis (SLTH) posits that randomly-initialized neural networks contain subnetworks (strong lottery tickets) that achieve competitive accuracy when compared to sufficiently small target networks, even those that have been trained. Empirical evidence for this phenomenon was first observed by Ramanujan et al. in 2020, spurring a line of theoretical research: Malach et al. (ICML ’20), Pensia et al. (NeurIPS ’20), da Cunha et al. (ICLR ’20), and Burkholz (ICML & ICLR ’22) have analytically proved formulations of the SLTH in various neural network classes and under different hypotheses. In this presentation, we provide an overview of the state-of-the-art theoretical research on the SLTH and its connection with the Random Subset Sum (RSS) problem in theoretical computer science. While previous works on the SLTH ensure that the strong lottery ticket can be obtained via unstructured pruning, we demonstrate how recent advances in the multidimensional generalization of the RSS problem can be leveraged to obtain forms of structured pruning. Additionally, we highlight how refining the RSS results would yield tighter formulations of the SLTH. This presentation is based on a joint work with A. Da Cunha and E. Natale appeared at NeurIPS 2023. Federico Fusco: The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations. We study the problem of regret minimization for a single bidder in a sequence of first-price auctions where the bidder discovers the item’s value only if the auction is won. Our main contribution is a complete characterization, up to logarithmic factors, of the minimax regret in terms of the auction’s transparency, which controls the amount of information on competing bids disclosed by the auctioneer at the end of each auction. Our results hold under different assumptions (stochastic, adversarial, and their smoothed variants) on the environment generating the bidder’s valuations and competing bids. These minimax rates reveal how the interplay between transparency and the nature of the environment affects how fast one can learn to bid optimally in first-price auctions. The talk is based on a joint work with Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, and Stefano Leonardi, which will appear at STOC 2024. Matteo Quattropani: Mixing of the Averaging process on graphs and hypergraphs. The Averaging process is a mass redistribution process over the vertex set of a graph or, more generally, a hypergraph. Given a (hyper)graph G, the process starts with a non-negative mass associated with each vertex. At each discrete time step, one of the (hyper)edges of G is sampled at random and the total mass associated with the vertices of the chosen (hyper)edge is equally redistributed among its vertices. Clearly, as time grows to infinity, the state of the system will converge to a flat configuration in which all the vertices have the same mass. This very simple process appeared in different literatures under various names, and it was introduced to the probabilistic community by Aldous and Lanoue in 2012. However, until a few years ago, there were no sharp quantitative results on the time needed to reach equilibrium. Indeed, the analysis of this process requires different tools compared to the classical Markov chain framework, and even in the case of seemingly straightforward geometries—such as the complete graph or the cycle—it can be handled only by means of nontrivial probabilistic and functional analytic techniques. During the talk, I’ll give an overview of the problem and its difficulties, present the classes of examples that are currently settled, and mention some possible future directions of investigation. Based on joint work with Pietro Caputo and Federico Sau. Guido Schaefer: To Trust or Not to Trust: Assignment Mechanisms with Predictions. The realm of algorithms with predictions has led to the development of several new algorithms that leverage (potentially erroneous) predictions to enhance their performance guarantees. The challenge here is to devise algorithms that achieve optimal approximation guarantees as the prediction quality varies from perfect (consistency) to imperfect (robustness). This framework is particularly appealing in mechanism design contexts, where predictions might convey private information about the agents. In this talk, we present our recent results on the design of truthful mechanisms that leverage predictions to achieve improved approximation guarantees for several variants of the generalized assignment problem (GAP). We consider the private graph model introduced by Dughmi and Ghosh (2010), where the set of resources that an agent is compatible with is private information. We investigate GAP in the private graph model augmented with a prediction of the optimal assignment. We give a deterministic group-strategyproof mechanism that is (1 + 1/γ)-consistent and (1 + γ)-robust for the special case of bipartite matching, where γ ≥ 1 is some confidence parameter. We also prove that this is best possible. Remarkably, our mechanism draws inspiration from the renowned Gale-Shapley algorithm, incorporating predictions as a crucial element. For more general GAP variants, we introduce a unified greedy scheme and use randomization to derive universally group-strategyproof mechanisms that achieve improved consistency and robustness guarantees in expectation. Robin Vacus: Minority Dynamics: the Short and Winding Road to Consensus. The ”minority” rule is a peculiar opinion dynamics, which prompts agents to adopt the opinion least represented in a sample – in contrast to its far more famous and natural counterpart, the majority rule. Yet, as long as the sample size is large enough and communications happen in parallel, it proves to be an efficient way to reach agreement. Moreover, contrary to traditional consensus protocols, it demonstrates extreme sensitivity to even a small number of ”stubborn” individuals, enabling fast information propagation within the group. In this presentation, I will describe an analysis of convergence time, showcase simulation results, and discuss several open problems, shedding light on what is currently understood and what remains to be explored about this fascinating dynamic. This talk is based on a recent work with Luca Becchetti, Andrea Clementi, Francesco Pasquale, Luca Trevisan and Isabella Ziccardi, that was published in SODA 2024. Xavier Mathieu Raymond Venel: Weighted average-convexity in Cooperative Games. It is well known that the Shapley value of a convex game always belongs to the core. Looking for a weaker condition than convexity insuring that the Shapley value of a game lies in the core, Inarra and Usategui (1993) relaxed the convexity assumption by introducing the notion of average convexity. Assuming that weights are associated with the players, we generalize the notion of convexity and average-convexity for cooperative TU games to the notion of weighted average-convexity. We prove that if a game is weighted average-convex, then the corresponding weighted Shapley value is in the core. We then study the relations between weighted average-convexity, core-inclusion, and communication TU-games. We exhibit necessary and sufficient conditions on the underlying graph to preserve weighted average-convexity from any communication game to the associated Myerson restricted game, extending some previous results established in Slikker (1998). Joint work with Alexandre Skoda.

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