Recorded Colloquial Talk, Wednesday, 12 May, 2021, 4 pm (ZOOM): Stanislav Sobolevsky PDF Print

Next Colloquial Talk at our department - online ZOOM meeting.

Title:  Towards the Digital City: methods and applications of urban network analysis and AI
Speaker: Stanislav Sobolevsky

Time: Wednesday, 12 May, 2021, 4 pm.

Dr. Stanislav Sobolevsky will present his prior research as well as the project to start at our department under a recent MASH award, see the invitation link.

The growing scale, complexity, and dynamics of urban systems pose tremendous challenges within urban planning and operations. At the same time, the increasing pervasiveness of digital technology in facilitating urban activities generates a vast amount of data. This big urban data creates fresh opportunities to respond to urban challenges and gain an unparalleled understanding of complex urban systems. And recent network analysis and AI techniques help to address the complexity and interconnectedness of the urban data.
I will introduce the network analysis techniques used by my teams at NYU and MIT to study the spatio-temporal transactional data on human mobility and interactions, as well as their applications to smart urban planning and smart transportation solutions.
I further present the proposed cross-disciplinary research program I  look forward to implementing at MUNI: the Digital City Engine - a  unified, scalable analytic framework for multi-layered urban data and its methodological core - Urban Network AI - a novel fusion of network science and deep learning techniques. We shall discuss the methodological foundations of Urban AI as well as applications to predictive modeling and detection of patterns, impacts, and emergent phenomena in spatio-temporal networks of urban activity.

Record available HERE

Last Updated on Thursday, 13 May 2021 11:21
Online algebra seminar - May 13th, 1pm PDF Print

We will continue online on Thursday, May 13th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Nathanael Arkor

Higher-order algebraic theories and relative monads

There have traditionally been two ways to reason about universal algebraic structure categorically: via algebraic theories, and via monads. It is well known that the two are tightly related: in particular, there is a correspondence between algebraic theories and a class of monads on the category of sets.

Motivated by the study of simple type theories, Fiore and Mahmoud introduced second-order algebraic theories, which extend classical (first-order) algebraic theories by variable-binding operators, such as the existential quantifier ∃x of first-order logic; the differential operators d/dx analysis; and the λ-abstraction operator of the untyped λ-calculus. Fiore and Mahmoud estab- lished a correspondence between second-order algebraic theories and a second-order equational logic, but did not pursue a general understanding of the categorical structure of second-order algebraic theories. In particular, the possibility of a monad–theory correspondence for second- order algebraic theories was left as an open question.

In this talk, I will present a generalisation of algebraic theories to higher-order structure, in particular subsuming the second-order algebraic theories of Fiore and Mahmoud, and describe a universal property of the category of nth-order algebraic theories. The central result is a correspondence between (n + 1)th-order algebraic theories and a class of relative monads on the category of nth-order algebraic theories, which extends to a monad correspondence subsuming that of the classical setting. Finally, I will discuss how the perspective lent by higher-order algebraic theories sheds new light on the classical monad–theory correspondence.

This is a report on joint work with Dylan McDermott.

Last Updated on Wednesday, 12 May 2021 15:57
Online differential geometry seminar - May 17, 10am PDF Print

The seminar on differential geometry will continue with this lecture:

May 17, 10amonline on MS Teams

Join via this LINK.

Radoslaw Kycia (Masaryk university):

CoPoincare lemma and applications to physics


I will outline the construction of the homotopy operator for codifferential defined on Riemannian manifolds. This notion can be used to solve, in a star-shaped open subset, many equations of mathematical physics including Dirac, Maxwell and string theory problems. I will also present an intriguing correspondence between (co)homotopy operator and Clifford algebra. I will also discuss various incarnations of spinors that appear in the literature. The talk is based on the draft [2] and [1].

[1]Radoslaw Kycia, The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator, Results in Mathematics 75, 122 (2020)
[2] Radoslaw Kycia, The Poincare lemma for codifferential, anticoexact forms, and applications to physics, arXiv: 2009.08542 [math.DG]

Last Updated on Wednesday, 12 May 2021 15:54
MASH AWARD: Stanislav Sobolevsky PDF Print

MASH AWARD for our department:

Stanislav Sobolevsky, Associate Professor at the New York University, has been awarded the Advanced MASH Belarus Award with his project DIGITAL CITY aimed at building the Digital City Engine and the Urban Network Artificial Intelligence at our department. The project will serve as seed funding for activities in the hot area of Smart Cities, as well as Network Science in general.