Math Lecture

Spectral Network and Betti Lagrangians

December 3 (Wed) 14:00 - 16:00, 2025

Yoonjae Nho (General Welfare Assistant, Seongdong District Office, Republic of Korea)

In this talk I will discuss the interface of spectral network theory and real contact and symplectic topology. For the first hour, I will give an introduction to spectral network theory using the Berk-Nevins-Roberts example, and review symplectic topology. For the second hour, I will talk about how GMN (Gaiotto-Moore-Neitzke) network theory can be interpreted from a symplectic perspective. I will then give an introduction to weave theory, which allows one to construct certain Lagrangian generalizations of spectral curves. I will then explain how to combinatorially compute spectral networks, with some applications. This is based on joint work with Roger Casals [1].

Venue: via Zoom (Main Venue) / Seminar Room #359

Event Official Language: English

On ℓ_p-Vietoris-Rips complexes and blurred magnitude homology

October 7 (Tue) 11:00 - 13:00, 2025

Sergei O. Ivanov (Professor, Beijing Institute of Mathematical Sciences and Applications, China)

One of the main tools in topological data analysis is the notion of a persistence module. The most prominent example is the persistence module associated with the Vietoris–Rips complex of a finite metric space. On the other hand, the concept of magnitude has become increasingly well known in data analysis. Recently, Nina Otter introduced blurred magnitude homology, which is also a persistence module associated with a metric space. Govc and Hepworth showed that the magnitude of a finite metric space can be uniquely recovered from its blurred magnitude homology. For 1 ≤ p ≤ ∞, we define the ℓ_p-Vietoris–Rips complexes and the associated ℓ_p​-persistent homology of metric spaces, and we study their fundamental properties. We show that for p=∞ this theory recovers the classical theory of Vietoris–Rips complexes and their persistent homology, while for p=1 it recovers the theory of blurred magnitude homology.

Venue: 3F 345-347 Seminar Room, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Bousfield-Kan completion as a codensity ∞-monad

October 3 (Fri) 15:00 - 17:00, 2025

Sergei O. Ivanov (Professor, Beijing Institute of Mathematical Sciences and Applications, China)

In this talk we recall the theory of codensity monads in ordinary category theory and tell about its generalization to the ∞-category setting. In particular, we show that the codensity ∞-monad of a full subcategory D of an ∞-category C satisfies a universal property: it is the terminal D-preserving ∞-monad. As an application, we show that the classical Bousfield-Kan R-completion functor can be described as the codensity ∞-monad of the full subcategory K(R) in the ∞-category of spaces spanned by the empty space and the products of Eilenberg-MacLane spaces of R-modules. As a corollary, we obtain that the Bousfield-Kan R-completion is the terminal K(R)-preserving ∞-monad.

Venue: Seminar Room #359 (Main Venue) / via Zoom

Event Official Language: English

A first look at Floer homology

September 25 (Thu) 15:00 - 16:30, 2025

Zhe Wang (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

This is the first meeting of the reading seminar on mirror symmetry. The first goal is to we will cover is the theory of Fukaya category, which is an important construction in A-side of mirror symmetry. The goal is to able to handle this object in practice, for example, to understand structures of Fukaya categories of complex plane/ cylinder/ simple curves/surfaces. We will start from the paper "A beginner's introduction to Fukaya categories" by D. Auroux. To start with, we discuss Floer homology required for definition of the Fukaya category.

Venue: Seminar Room #359

Event Official Language: English

Colored Links and Topological Vortex Structures

May 23 (Fri) 16:00 - 17:45, 2025

Toni Annala (Dickson Instructor, Department of Mathematics, The University of Chicago, USA)

Topological vortices are intriguing defects that emerge in a wide range of physical systems, including Bose–Einstein condensates and liquid crystals. In this talk, I will describe how the global structure of such vortices can be captured pictorially using colored link diagrams—or more generally, colored embedded graphs. Through a variety of examples, I will illustrate how this framework can be used to classify and analyze vortex configurations. In particular, I will highlight conditions under which these structures are topologically protected, in the sense that they cannot decay into collections of disjoint loops without destroying the underlying phase of the system. These investigations naturally give rise to new topological invariants of colored links, which can be used to distinguish and classify such vortex structures.

Venue: Seminar Room #359

Event Official Language: English

Introduction to Public-Key Cryptography (10th)

April 9 (Tue) 13:30 - 15:30, 2019

Eren Mehmet Kıral (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Visiting Scientist (JSPS Research Fellow), Faculty of Science and Technology, Sophia University)

Venue: Seminar Room #160

Event Official Language: English

Introduction to Public-Key Cryptography (9th)

March 6 (Wed) 13:30 - 15:00, 2019

Eren Mehmet Kıral (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Visiting Scientist (JSPS Research Fellow), Faculty of Science and Technology, Sophia University)

Venue: Seminar Room #160

Event Official Language: English

Theory of Operator Algebras (9th)

March 5 (Tue) 15:30 - 16:30, 2019

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Title: An introduction to operator algebras Abstract: Operators are linear maps from a (usually an infinite dimensional) linear space (most frequently the Hilbert space) to itself, which is like matrices of infinite degree. Operators form an algebra by obvious addition and multiplication. Operators appear in most of the fields in mathematics, in algebra, in geometry, in analysis, ... Some of the key words at the beginning of these lectures are "spectral theory" "operator algebras" "Tomita-Takesaki theory". These lectures are for non-professional people.

Venue: Seminar Room #160

Event Official Language: Japanese

Theory of Operator Algebras (8th)

March 5 (Tue) 14:00 - 15:00, 2019

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Title: An introduction to operator algebras Abstract: Operators are linear maps from a (usually an infinite dimensional) linear space (most frequently the Hilbert space) to itself, which is like matrices of infinite degree. Operators form an algebra by obvious addition and multiplication. Operators appear in most of the fields in mathematics, in algebra, in geometry, in analysis, ... Some of the key words at the beginning of these lectures are "spectral theory" "operator algebras" "Tomita-Takesaki theory". These lectures are for non-professional people.

Venue: Seminar Room #160

Event Official Language: Japanese

Introduction to Public-Key Cryptography (8th)

February 7 (Thu) 13:30 - 15:00, 2019

Eren Mehmet Kıral (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Visiting Scientist (JSPS Research Fellow), Faculty of Science and Technology, Sophia University)

Venue: Seminar Room #160

Event Official Language: English

Introduction to Public-Key Cryptography (7th)

January 18 (Fri) 15:00 - 17:00, 2019

Eren Mehmet Kıral (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Visiting Scientist (JSPS Research Fellow), Faculty of Science and Technology, Sophia University)

Venue: Seminar Room #160

Event Official Language: English

Theory of Operator Algebras (7th)

January 10 (Thu) 10:30 - 12:00, 2019

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Title: An introduction to operator algebras Abstract: Operators are linear maps from a (usually an infinite dimensional) linear space (most frequently the Hilbert space) to itself, which is like matrices of infinite degree. Operators form an algebra by obvious addition and multiplication. Operators appear in most of the fields in mathematics, in algebra, in geometry, in analysis, ... Some of the key words at the beginning of these lectures are "spectral theory" "operator algebras" "Tomita-Takesaki theory". These lectures are for non-professional people.

Venue: Seminar Room #160

Event Official Language: Japanese

Theory of Operator Algebras (6th)

December 20 (Thu) 15:30 - 17:00, 2018

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Title: An introduction to operator algebras Abstract: Operators are linear maps from a (usually an infinite dimensional) linear space (most frequently the Hilbert space) to itself, which is like matrices of infinite degree. Operators form an algebra by obvious addition and multiplication. Operators appear in most of the fields in mathematics, in algebra, in geometry, in analysis, ... Some of the key words at the beginning of these lectures are "spectral theory" "operator algebras" "Tomita-Takesaki theory". These lectures are for non-professional people.

Venue: Seminar Room #160

Event Official Language: Japanese

Theory of Operator Algebras (5th)

November 8 (Thu) 13:30 - 15:00, 2018

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Venue: Seminar Room #160

Event Official Language: Japanese

Theory of Operator Algebras (4th)

October 18 (Thu) 15:30 - 17:00, 2018

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Venue: Seminar Room #160

Event Official Language: Japanese

Theory of Operator Algebras (3rd)

July 12 (Thu) 15:30 - 17:00, 2018

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Venue: Seminar Room #160

Event Official Language: English

Introduction to Public-Key Cryptography (6th)

July 11 (Wed) 10:30 - 12:00, 2018

Eren Mehmet Kıral (Visiting Researcher, RIKEN Center for Advanced Intelligence Project (AIP))

Venue: Seminar Room #160

Event Official Language: English

Computational Algebraic Statistics and its Applications

June 26 (Tue) 10:00 - 16:30, 2018

Satoshi Aoki (Professor, Department of Mathematics, Kobe University)

Lecture 1 (10:00-11:30) An introduction of Groebner bases of polynomial rings Lecture 2 (13:00-14:30) Groebner bases theory in design of experiments Lecture 3 (15:00-16:30) Groebner bases theory in sampling problems of contingency tables This introductory lecture is about statistical theory from the point of view of the computational algebraic statistics, in particular the applications of Groebner bases. The statistical theory is a fundamental tool in natural science, social science and humanities, and the Groebner basis is a topic related to multi-variable polynomials. The Lecture will start from an introduction to the Groebner basis which would have wide applications in mathematics, physics, biology, chemistry, engineering, information science and computer science. Therefore, we welcome scientists in any field who are interested in this subject. The event official language is Japanese (slides and writing are in English).

Venue: #535-537, 5F, Main Research Building

Event Official Language: Japanese

Theory of Operator Algebras (2nd)

June 21 (Thu) 15:30 - 17:00, 2018

Yosuke Kubota (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Please note that the date and time of the 2nd lecture has been changed from May 21 10:30 to June 21 15:30.

Venue: Seminar Room #160

Event Official Language: English

Introduction to Public-Key Cryptography (5th)

June 21 (Thu) 10:30 - 12:00, 2018

Eren Mehmet Kıral (Visiting Researcher, RIKEN Center for Advanced Intelligence Project (AIP))

Venue: Seminar Room #160

Event Official Language: English