# Category Archives: Uncategorized

# STEM for Industry

Baltic Institute of Mathematics under the patronage of Prof. Jerzy Buźek in partnership with PZU S.A. and the Institute of Mathematics of NAS of Ukraine as a part of Polish-Ukrainian Science and Culture Forum for the Next Generation announces the **STEM for Industry challenge**

High school students are eligible to participate in our science challenge!

The process is easy: Industry companies propose a scientific challenge, and students work on a solution. The best solutions will compete for a grant worth 1200 PLN and the opportunity to publish the results in a research publication.

To sign up, please fill in the registration form

# Polish-Ukrainian Science and Culture Forum for the Next Generation

# Discover Polish universities and the opportunities they offer for Ukrainian students.

# Summer School & Workshop Wisla 23

The Summer School & Workshop Wisla 23 will bring together students, researchers, and practitioners from all over the world to share groundbreaking insights in AI, mathematics, and computer science. The event will take place from **August 21 - September 1, 2023 **in a virtual form,** **and will combine lectures by experts in the field and talks by participants. This year's theme is *Mapping the Interdisciplinary Horizons of AI: Safety, Functional Programming, Information Geometry, and Beyond.*

### LECTURES

**Scott Aaronson**(The University of Texas at Austin, USA)

**AI Safety: Leaning Into Uninterpretability**I'll share some thoughts about AI safety, shaped by a year's leave at OpenAI to work on the intersection of AI safety and theoretical computer science. I'll discuss what I've worked on, including a scheme for watermarking the outputs of Large Language Models such as GPT, as well as proposals such as cryptographic backdoors and a theory of AI acceleration risk.

**Seth Baum**(Global Catastrophic Risk Institute, University of Cambridge, USA)

**Social and Philosophical Dimensions of AI Alignment**Successful AI alignment requires three steps: (1) concept(s) for what, if anything, to align AI to; (2) design(s) for how to implement the concept(s) in one or more AI systems; and (3) the usage, by human developers of AI systems, of these design(s) instead of other, less suitable design(s). Step (1) is mainly a matter of moral philosophy; step (2) is mainly a matter of computer science; and step (3) is mainly a matter of social science and politics. My lecture(s) will cover steps (1) and (3).

(*Olle Häggström**Chalmers University of Technology, Sweden*)

**AI risk and AI alignment**The planetary dominance over other species that humanity has attained has very little to do with muscular strength and physical endurance: it is all about intelligence. This makes the present moment in history, when we are automating intelligence and handing over this crucial skill to machines, the most important ever. The research area that has become known as AI alignment deals with how to make sure that the first superintelligent machines have goals and values that are sufficiently aligned with ours and that sufficiently prioritize human flourishing. This needs to succeed, because otherwise we face existential catastrophe. In these lectures I will outline key challenges in AI alignment, what is being done to solve them, and how all this relates to the breakneck speed at which AI is presently advancing.

TBA**Anders Sanberg**(Future of Humanity Institute, University of Oxford, UK)

(*Patrik Jansson**Chalmers University of Technology, Sweden*)

The main idea behind this minicoure is to encourage the students to approach mathematical domains from a functional programming perspective. We will learn about the language Haskell; identify the main functions and types involved; introduce calculational proofs; pay attention to the syntax of mathematical expressions; and, finally, to organize the resulting functions and types in domain-specific languages.**Domain-Specific Languages of Mathematics**

*Frank Nielsen**(Sony Computer Science Laboratories, Japan)*

**Introduction to Information Geometry, Recent Advances, and Applications.**Information geometry primarily studies the geometric structures, dissimilarities, and statistical invariance of a family of probability distributions called the statistical model. A regular parametric statistical model can be geometrically handled as a Riemannian manifold equipped with the Fisher metric tensor which induces the Fisher-Rao geodesic distance. This Riemannian structure on the Fisher-Rao manifold was later generalized by a dual structure based on pairs of torsion-free affine connections coupled to the Fisher metric: The α-geometry. This dual structure casts light on the close interaction between statistical estimators in inference (maximum likelihood) and parametric statistical models (exponential families obtained from the principle of maximum entropy), and brings into play a generalized Pythagorean theorem useful to prove uniqueness of information projections. We will illustrate applications of information geometry in statistics, information theory, computer vision and pattern recognition, and learning of neural networks. The second part of the minicourse will present recent advances in information geometry and its applications.

(*Dmitri Alekseevsky**University of Hradec Králové, Czech Republic*)These lectures will provide a comprehensive overview of information processing. We will start with information processing in early vision in static and geometric models of the primary visual cortex. Then, we will explore information processing in vision in dynamics. Finally, we gonna talk about the information geometry of Chentsov-Amari and homogeneous convex cones.**Neurogeometry of Vision and Information Geometry of Homogeneous Convex Cones**

(*Frédéric Barbaresco**Thales Land and Air Systems,**France*)**Symplectic Foliation Structures of Information Geometry for Lie Groups Machine Learning**We present a new symplectic model of Information Geometry based on Jean-Marie Souriau's Lie Groups Thermodynamics. Souriau model was initially described in chapter IV “Statistical Mechanics” of his book “Structure of dynamical systems” published in 1969. This model gives a purely geometric characterization of Entropy, which appears as an invariant Casimir function in coadjoint representation, characterized by Poisson cohomology. Souriau has proved that we can associate a symplectic manifold to coadjoint orbits of a Lie group by the KKS 2-form (Kirillov, Kostant, Souriau 2-form) in the affine case (affine model of coadjoint operator equivariance via Souriau's cocycle), that we have identified with Koszul-Fisher metric from Information Geometry. Souriau established the generalized Gibbs density covariant under the action of the Lie group. The dual space of the Lie algebra foliates into coadjoint orbits that are also the Entropy level sets that could be interpreted in the framework of Thermodynamics by the fact that dynamics on these symplectic leaves are non-dissipative, whereas transversal dynamics, given by Poisson transverse structure, are dissipative. We will finally introduce Gaussian distribution on the space of Symmetric Positive Definite (SPD) matrices, through Souriau's covariant Gibbs density by considering this space as the pure imaginary axis of the homogeneous Siegel upper half space where Sp(2n,R)/U(n) acts transitively. We will also consider Gibbs density for Siegel Disk where SU(n,n)/S(U(n)xU(n)) acts transitively. Gauss density of SPD matrices is then computed through Souriau's moment map and coadjoint orbits. Souriau’s Lie Groups Thermodynamics model will be further explored in European COST network CaLISTA and European HORIZON-MSCA project CaLIGOLA.

(*Noémie Combe**Max Planck Institute for Mathematics in Sciences, Germany*)

**Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory**With the rapid progress of machine learning, artificial intelligence and data sciences, the topic of information geometry is an important domain of research. We aim at introducing the topic of information geometry, as well as presenting some recent progress in this domain. Differential geometry and algebraic aspects shall be developed. The new tight relation between the information geometry and topological field theory will be discussed

**MATERIALS **(available only for admitted participants)

### CALL FOR CONTRIBUTIONS

The school will provide participants with an opportunity to interact with their colleagues and well-known researchers in the field. Each participant could make a talk about recent research and get independent and constructive feedback on her/his current research and future research directions. **Materials from the school and workshop will be published by Springer Nature. All contributions are subject to peer review.**

**Org. Committee
**J. de Lucas, M. Roop, J.Szmit, R.Zawadzki, M.Ulan, M. Wojnowski

# An invitation to symplectic geometry and classical mechanics.

**Online**

*May 18, 2021 11:00 - 12:00 CET*

**Speaker:**

Javier de Lucas Araujo (Assistant professor at the Department of Mathematical Methods in Physics of the Faculty of Physics of the University of Warsaw)

**Abstract:**

In this talk, I will introduce some notions and results on symplectic geometry and their applications to classical mechanics. Although omitting technical proofs, I will explain the main ideas and results about this theory and its applications. In detail, I will comment on the definition of symplectic manifolds, Hamiltonian vector fields and functions, Poisson brackets, momentum maps, and the Marsden-Weinstein theorem. More physically, I will explain how these structures explain the Hamilton equations of a classical mechanical system and how they are used to study systems with symmetries.

** Registration:**To register, please, fill in the

**registration form.**

**Organizers:**

- Baltic Institute of Mathematics (Warsaw, Poland, http://www.baltinmat.com)

- Institute of Mathematics of NAS of Ukraine (Kyiv, Ukraine, http://www.imath.kiev.ua)

# Symplectic Methods and Dynamical Systems

**Online**

*January 15, 2021 11:00 - 12:00 CET*

**Speaker:**

Javier de Lucas Araujo (Assistant professor at the Department of Mathematical Methods in Physics of the Faculty of Physics of the University of Warsaw)

**Abstract:**

This talk provides a brief introduction to symplectic geometry and its applications to dynamical systems. In particular, I will explain the most fundamental notions on symplectic geometry such as the Darboux theorem, the canonical symplectic structure on the cotangent bundle, and the main properties of the so-called Hamiltonian vector fields. Concerning the applications of symplectic geometry to dynamical systems, the Liouville theorem, the Gromov’s non-squeezing theorem, and the main properties of the referred to as integrable Hamiltonian systems will be analysed.

**Slides & Recording ( Password Available Upon Request)
**

**Organizers:**

- Baltic Institute of Mathematics (Warsaw, Poland, http://www.baltinmat.com)

- Institute of Mathematics of NAS of Ukraine (Kyiv, Ukraine, http://www.imath.kiev.ua)

# Summer Camp Green Futurum 2020

**Summer, mountains, math! What can be better?**

Do you enjoy math, physics, and programming?

Join the international children math and physics community **BIM**. We invite you to have two unforgettable weeks (21 August - 4 September 2020) in a summer math camp for students of 1-8 grades which takes place in a small Polish town at the foot of the mountains. We also invite students of 1-4 grades (ages 6-11) to our school together with parents.

The most interesting problems and math puzzles as well as twisted origami are waiting ahead. Every one of you can try being a scientist, an engineer or even a film director.

**We will show where and how math appears in real life. **Are you with us?

This year edition will be focused on a connection between **Mathematics and Sustainability.**

For more details on Futurum STREAM Camps , please follow the link below:

http://baltinmat.com/events/event/futurum-stream-camp/

# GAADE Conference

Conference “Geometry, Algebra and Analysis of Differential Equations" will be held in conjunction with the Summer School & Workshop Wisla 20.

*Wisła, Poland
*

*August 14 – August 16, 2020*

The **ARRIVAL DAY** is August 13.

The **DEPARTURE DAY** is August 16.

**Conference fee is 750 EUR
**

**Deadline for registration and payment is June 1, 2020.**

*The fee includes meals and accommodation in a single room.
*

*Interested participants are requested to send an e-mail to*

**office@baltinmat.eu**or fill the registration form.*Your request will be considered by the Organizing Committee.*

**Selected materials of the conference will be published by Springer Nature.**

Organising Committee:

V. Lychagin, V. Rubtsov, J. Szmit, J. Slovák, M. Ulan, R.Zawadzki

* *

# Summer School & Workshop Wisla 20

Groups, invariants, integrals and their applications to fluid dynamics and thermodynamics

EMS SUMMER SCHOOL IN APPLIED MATHEMATICS (ESSAM)

*Wisła, Poland
*

*August 17 – August 27, 2020*

**Due to the COVID-19 pandemics, the Wisla Summer School & Workshop will be organized in a hybrid model: in-person or remote online participation.**

**The topic of the forthcoming school:
**Groups, invariants, and integrals.

The goal of the forthcoming school is to present recent results in differential geometry related to nonlinear PDEs and mathematical physics. The lectures will focus on Lie groups and pseudogroups which play an important role in these fields, and we will discuss different ways of studying their orbit spaces. Two main topics are Poisson algebras and differential invariants. The theory will be illustrated by examples from algebraic and differential geometry, fluid dynamics, and thermodynamics.

The school will provide young researchers with an opportunity to interact with their colleagues and well-known researchers in the field. Selected materials of the school and workshop will be published by Springer Nature.

**The speakers will be:
**

**Lychagin Valentin**(University of Tromsø, Norway)*Differential contra algebraic invariants.*

**Rubtsov Volodya **(University of Angers, France)

Poisson algebras.

**Schneider Eivind**** ***(University of Hradec Králové, Czech Republic)*

Differential invariants of Lie pseudogroups.

**ARRIVAL DAY**is August 16.

The **DEPARTURE DAY** is August 27.

School fee for in-person participation is 450 EUR for Early bird registration (until July 15, 2020), **550 EUR for registration after July 15, 2020 until August 1, 2020.
The school fee for remote online participation is 100 EUR.**

*The fee for in-person includes meals, accommodation (2-3 beds rooms with private bathroom), and lectures. Accommodation in a single room costs an additional 100 EUR.*

The fee for remote online participation includes lectures and covers technical issues.

*To apply please send an e-mail to office@baltinmat.eu or fill the registration form.
*

*Your request will be considered by the Organizing Committee.*

**Financial Support**

We expect that some **support** will be available to fund students and other young researchers. If you are requesting financial support, please complete the registration form** **and send a pdf of your CV as soon as possible.

Org. Committee:

R. Kycia, J. de Lucas, E. Schneider, J.Szmit, R.Zawadzki, M.Ulan, M. Wojnowski

#######################################################################

**Proceedings of Summer School & Workshop Wisla 20
**Materials of the school and workshop will be published by Springer Nature.

The school will provide young researchers with an opportunity to interact with their colleagues and well-known researchers in the field:

- each participant could make a talk about recent research or present a poster

- each participant will get independent and constructive feedback on her/his current research and future research directions

- a decision about including participant’s work to the book will be made based on experts’ feedback

- each participant will also be given an opportunity to improve her/his work during the school