IUT seminars in Geometry, Topology and PDE (IGTP)
About: IGTP is a seminar held on regular basis which hosts 1) single seminar or colloquium talks or series of talks about original research or 2) mini-courses or workshops in a broad range of topics centering around Geometry, Topology, Analysis and PDE. This event is geared towards a more specialized audience.
Organizer:
Sajjad Lakzian (Isfahan University of Technology)
Message: Send me email requests should you wish to give a talk at our seminar or suggest a speaker.
Fall 2023:
| Talk Number | Time and Date | Speaker | Affiliation | Title |
|---|---|---|---|---|
| 1) | Nov. 30th, 2023 9 Azar, 1402 | Christine Breiner | Brown University | Harmonic Maps to Metric Spaces with Upper Curvature Bounds |
| 2) | Dec. 11th, 2023 20 Azar, 1402 | Byungdo Park | Chungbuk University | Differential Cohomology and Gerbes: I |
| 3) | Dec. 18th, 2023 27 Azar, 1402 | ------ | ------ | Differential Cohomology and Gerbes: II |
| 4) | Dec. 25th, 2023 4 Dey, 1402 | ------ | ------ | Differential Cohomology and Gerbes: III |
Spring 2024:
| Talk Number | Time and Date | Speaker | Affiliation | Title |
|---|---|---|---|---|
| 5) | April 24th, 2024 5 Ordibehesht, 1403 | Yu Kitabeppu | Kumamoto University | Coarse Ricci Curvature on Hypergraphs |
| 6,7) | May 27th, 2024 7 Khordad, 1403 | Sadok Kallel | American Univ. of Sharjah & Laboratoire Painlevé, Lille 1, France | Topology and Geometry of Configuration Spaces I, II |
| 8,9) | May 28th, 2024 8 Khordad, 1403 | ------ | ------ | Topology and Geometry of Configuration Spaces III, IV |
Fall 2025:
| 10) | Oct. 3rd, 2024 12 Mehr, 1403 | Xinrui Zhao | MIT | Unique continuation problem on RCD spaces |
| 11) | Nov. 7th, 2024 17 Aban, 1403 | Brian Allen | Lehman College, City University of New York | On the Scalar Compactness Conjecture in the Conformal Case |
| 12) | Nov. 21st, 2024 1 Azar, 1403 | Christian Ketterer | Maynooth University | Gluing spaces that satisfy the Bakry-\'Emery condition |
| 13) | Dec. 5th, 2024 15 Azar, 1403 | Demetre Kazaras | Michigan State University | Scalar curvature and codimension 2 collapse |
Spring 2025:
| 14) | May 8th, 2025 18 Ordibehesht, 1404 time: 4:30 - 5:30 Tehran Time | Haotian Wu | The University of Sydney | Asymptotic behavior of unstable perturbations of the Fubini–Study metric in Ricci flow |
Talk Details:
1)
Date: Nov. 30th, 2023 (9 Azar, 1402)
Speaker: Christine Breiner, Brown University
Title: Harmonic Maps to Metric Spaces with Upper Curvature Bounds
Abstract: A natural notion of energy for a map is given by measuring how much the map stretches at each point and integrating that quantity over the domain. Harmonic maps are critical points for the energy and existence and compactness results for harmonic maps have played a major role in the advancement of geometric analysis. Gromov-Schoen and Korevaar-Schoen developed a theory of harmonic maps into metric spaces with non-positive curvature in order to address rigidity problems in geometric group theory. In this talk we consider harmonic maps into metric spaces with upper curvature bounds. We will define these objects, state some key results, and demonstrate their application to rigidity and uniformization problems.
Venue: online
2,3,4) (Minicourse)
Time: Mondays 4pm-4:50pm Tehran Time (21:30 - 22:20 Seoul time)
Dates:
Session I : Dec. 11th, 2023 (20 Azar, 1402)
Session II : Dec. 18th, 2023 (27 Azar, 1402)
Session III: Dec. 25th, 2023 (4 Dey, 1402)
Speaker: Byungdo Park, Chungbuk University, South Korea
Title: Differential Cohomology and Gerbes: An Introduction to Higher Differential Geometry
Abstract: Differential cohomology is a topic that has been attracting considerable interest. Many interesting applications in mathematics and physics have been known; description of WZW terms, string structures, study of conformal immersions, classifications of Ramond-Ramond fields to list a few, and it is also an interesting application of the theory of infinity categories. I will try to give an audience-friendly overview of differential cohomology and a classification of higher line bundles (a. k. a. U(1)-banded gerbes) with connection. I will start from scratch and assume only some basic differential geometry and algebraic topology so that it would be accessible to most graduate students.
Venue: online
5)
Time: Wednesday 4pm-5:00pm Tehran Time (20:30 - 21:30 Tokyo Time)
Dates: April 24th, 2024 (5 Ordibehesht, 1403)
Speaker: Yu Kitabeppu, Kumamoto University, Japan
Title: Coarse Ricci Curvature on Hypergraphs
Abstract: There are several notions of (lower bound of) Ricci curvature on discrete spaces. I will give a new notion of Ricci curvature on hypergraphs related to the Lin- Lu-Yau’s coarse Ricci curvature on graphs (LLY curvature for short). The definition of LLY curvature defined by using the Markov chain on vertex set on graph. Since the Laplacian of hypergraph is non-linear, it is difficult to define Ricci curvature on hypergraphs in the same way as LLY one. In my talk, I explain how to overcome such difficulties and tell the geometric consequences of assuming lower bound of Ricci curvature. These are based on two joint works with M.Ikeda-Y.Takai-T.Uehara, and with E.Matsumoto.
Venue: online
6--9) (Minicourse)
Schedule:
Session I : Date: Monday, May. 27th, 2024 (7 Khordad, 1403), Time: 10:00 -- 11:30
Session II : Date: Monday, May. 27th, 2023 (7 Khordad, 1403). Time: 15:00 -- 16:30
Session III : Date: Tuesday, May. 28th, 2024 (8 Khordad, 1403). Time: 10:00 -- 11:30
Session IV : Date: Tuesday, May. 28th, 2024 (8 Khordad, 1403). Time: 15:00 -- 16:30
Speaker: Sadok Kallel: American Univ. of Sharjah & Laboratoire Painlevé, Lille 1, France
Title: Topology and Geometry of Configuration Spaces
Abstract: Configuration spaces of distinct points have seen an explosion in interest and in the number of publications. Applications have long gone beyond algebraic topology to encompass all modern aspects of geometry, analysis, and mathematical physics, further making incursions into the applied science fields. This series of lectures will introduce and explain some of the many constructions and results in the theory, with an eye on applications.
Venues:
In Person: Kharazmi Conference Room, Department of Mathematics, IUT
Online: ...
10)
Schedule:
Date: Thursday, Oct. 3rd, 2024 (12 Mehr, 1403)
Time: 5:00pm-6:00pm Tehran Time (8:30am - 9:30am EST)
Speaker: Xinrui Zhao, MIT
Title: Unique continuation problem on RCD spaces
Abstract: In this talk we will sketch the proof of the unique continuation property of harmonic functions and caloric functions on any RCD(K,2) spaces and a counterexample for the strong unique continuation property of harmonic function on an RCD(K,4) space. This characterizes one of the significant differences between RCD spaces and smooth manifolds. We will also talk about some related open problems. The talk is based on joint works with Qin Deng.
Venue: online
11)
Schedule:
Date: Thursday, Nov. 7th, 2024 (17 Aban, 1403)
Time: 5:00pm-6:00pm Tehran Time (9:30am - 10:30am EST)
Speaker: Brian Allen, Lehman College, City University of New York
Title: On the Scalar Compactness Conjecture in the Conformal Case
Abstract: Understanding in what sense scalar curvature is flexible versus rigid has been an important area of investigation in geometric analysis. We have many rigidity phenomena involving scalar curvature understood and we are recently turning to the question of stability. One question in this direction asks, If we take a sequence of Riemannian manifolds with non-negative scalar curvature, then what additional hypotheses need to be added to ensure that a subsequence exists which converges to a metric space with some notion of weakly non-negative scalar curvature? In this talk we will investigate this question in the case where the sequence of Riemannian manifolds is conformal to the round sphere.
Venue: online
12)
Schedule:
Date: Thursday, Nov. 21st, 2024 (1 Azar, 1403)
Time: 5:00pm-6:00pm Tehran Time (1:30pm - 2:30pm Dublin Time)
Speaker: Christian Ketterer, Maynooth University
Title: Gluing spaces that satisfy the Bakry-\'Emery condition
Abstract: I will present conditions such that the glued space of two weighted Riemannian manifolds with boundary and a Bakry-Emery lower Ricci curvature bound satisfies a curvature-dimension condition. For the case of classical Ricci lower bounds this follows from a theorem of Perelman. Moreover these conditions in return are implied by a curvature-dimension condition for the glued space, and this is new even for the unweighted case.
Venue: online
13)
Schedule:
Date: Thursday, Dec. 5th, 2024 (15 Azar, 1403)
Time: 5:00pm-6:00pm Tehran Time (8:30am - 9:30am EST)
Speaker: Demetre Kazaras, Michigan State University
Title: Scalar curvature and codimension 2 collapse
Abstract: This talk is about the structure of Riemannian 3-manifolds satisfying a lower bound on their scalar curvature. These manifolds are toy models for spatial geometry in general relativity. Our motivational question will be "How flat is an isolated gravitational system with very little total mass?" Objects like gravity wells and black holes can distort geometry without accumulating much mass, making this a subtle question. In addition to discussing progress, I will present a "drawstring" construction, which modifies a manifold near a given curve, reducing its length with negligible damage to a scalar curvature lower bound. Unexpected examples are produced with relevance to a few problems. This construction extends ideas of Basilio-Dodziuk-Sormani and Lee-Naber-Neumayer, and is based on joint work with Kai Xu.
Venue: online
14)
Schedule:
Date: Thursday, May 8th, 2025 (18 Ordibehesht, 1404)
Time: 4:30pm-5:30pm Tehran Time
Speaker: Haotian Wu, The University of Sydney
Title: Asymptotic behavior of unstable perturbations of the Fubini–Study metric in Ricci flow
Abstract: The Ricci flow can be regarded as a dynamical system on the space of Riemannian metrics. It is important to identify and study its fixed points, which are generalized Einstein metrics known as Ricci solitons. A prominent example of a Ricci soliton is the Fubini–Study metric on complex projective space. Kröncke has shown that the Fubini–Study metric is an unstable generalized stationary solution of Ricci flow. This raises an interesting question: What happens to Ricci flow solutions that start at arbitrarily small but unstable perturbations of the Fubini–Study metric? In a joint work with Garfinkle, Isenberg and Knopf, we carry out numerical simulations which indicate Ricci flow solutions originating at unstable perturbations of the Fubini–Study metric develop local singularities modeled by the FIK shrinking soliton discovered by Feldman, Ilmanen and Knopf.
Venue: https://meet.google.com/wha-yopd-trc