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IUT Mathematics and Statistics Research Seminars (IMSRS)
IUT Mathematics and Statistics Research Seminars (IMSRS)
About: IMSRS is a semi-periodic event which hosts single talks or series of talks about original research works as well as mini-courses, all from researchers working in various fields of Mathematics and Statistics.
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.
| Talk Number | Time and Date | Speaker | Affiliation | Title | Abstract |
|---|---|---|---|---|---|
| 1) |
Oct. 28th, 2023 6 Aban, 1402 |
Mojtaba Fadavi | University of Calgary | An Overview of Modern Cryptography | abstract |
| 2) |
Nov. 20th, 2023 29 Aban, 1402 |
Milad Karimi | University of Göttingen | X-Ray Holographic Imaging Using Intensity Correlations | abstract |
| 3) |
Nov. 30th, 2023 9 Azar, 1402 |
Christine Breiner | Brown University | Harmonic Maps to Metric Spaces with Upper Curvature Bounds | abstract |
| 4) |
Dec. 4th, 2023 13 Azar, 1402 |
Reza Mokhtari | Isfahan Univ. of Tech. | Solving Some Elliptic Equations Using Deep Learning Approaches Based on the Hybridized Discontinuous Galerkin Method |
abstract |
| 5) |
Dec. 11th, 2023 20 Azar, 1402 |
Byungdo Park | Chungbuk University |
Differential Cohomology and Gerbes: I |
abstract |
| 6) |
Dec. 18th, 2023 27 Azar, 1402 |
------ | ------ |
Differential Cohomology and Gerbes: II |
abstract |
| 7) |
Dec. 25th, 2023 4 Dey, 1402 |
------ | ------ |
Differential Cohomology and Gerbes: III |
abstract |
| 8) |
April 24th, 2024 5 Ordibehesht, 1403 |
Yu Kitabeppu | Kumamoto University | Coarse Ricci Curvature on Hypergraphs | abstract |
Talk Details:
1)
Date: Oct. 28th, 2023 (6 Aban, 1402)
Speaker: Mojtaba Fadavi, University of Calgary
Title: An Overview of Modern Cryptography
Abstract: Digital signature schemes are cryptographic tools that play a pivotal role in verifying the authenticity and integrity of digital documents, transactions, and messages. (EC)DSA and RSA are widely used digital signature schemes, both of which are proven to be insecure in the presence of large-scale quantum computers due to Shor’s polynomial-time quantum algorithms. In response to this significant development, the National Institute of Standards and Technology (NIST) issued a noteworthy announcement in 2015, marking the initiation of a transition to Post-Quantum (PQ) cryptographic schemes. In other words, this strategic move arose from growing concerns about potential threats posed by quantum computers to established cryptographic systems. In this talk, we first review some related concepts, then we will examine some post-quantum schemes, including Hash-based signature schemes and Isogeny-based Key Exchange Protocols.
2)
Date: Nov. 20th, 2023 (29 Aban, 1402)
Speaker: Milad Karimi, University of Göttingen
Title: X-Ray Holographic Imaging Using Intensity Correlations
Abstract: Holographic coherent X-ray imaging enables nanoscale imaging of biological cells and tissue, rendering both phase and absorption contrast, i.e. real and imaginary part of the refractive index. A main challenge of this imaging technique is radiation damage. We present a different modality of this imaging technique using a partially coherent incident beam and time resolved intensity measurements based on new measurement technologies. This enables the acquisition of intensity correlations in addition to the commonly used expectations of intensities. In this talk, we explore the information content of these intensity correlations, analytically showing that in the linearized model both phase and absorption contrast can uniquely be determined by the intensity correlation data. The uniqueness theorem is derived by multi-dimensional Kramers-Kronig relations. For regularized reconstruction it is important to take into account the statistical distribution of the correlation data. In principle, the measured intensity data are described by a so-called Coxprocesses, roughly speaking a Poisson process with random intensity. For medium size data sets, we use adaptations of the iteratively regularized Gauss-Newton method and the FISTA method as reconstruction methods. Our numerical results even in the full nonlinear model confirm that both phase and absorption contrast can jointly be reconstructed from only intensity correlations without the use of average intensities. Although these results are encouraging concerning the information content of the new intensity correlation data, the increased dimensionality of these data causes severe computational challenges.
3)
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.
4)
Date: Dec. 4th, 2023 (13 Azar, 1402)
Speaker: Reza Mokhtari, Isfahan University of Technology
Title: Solving Some Elliptic Equations Using Deep Learning Approaches Based on the Hybridized Discontinuous Galerkin Method
Abstract: During the talk, two approaches using deep neural networks (DNNs) based on the hybridized discontinuous Galerkin (HDG) method are presented. The HDG method is commonly known to have dependencies on mesh-grid points, which can make it challenging to solve problems with complex geometry in higher dimensions. One of our recent researchs has led to the development of two artificial neural network approaches that overcome the limitations of the classical HDG methods. The first approach, called DNN-HDG, directly approximates the solutions of the variational form using neural networks after applying the HDG method with a suitable definition of numerical flux and trace. The second approach, known as DNN-HDG-II, is more compatible with the classical HDG method, where the solutions are considered as linear combinations of the trial functions, and the coefficients are approximated using the neural network technique. We have proven that the loss function corresponding to these proposed DNN-HDG methods for solving elliptic equations converges to zero as the mesh step size reduces. Additionally, we have demonstrated through several examples that the DNN-HDG methods can efficiently and accurately extract solution patterns in one, two, and three dimensions.
5,6,7) (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: https://meet.google.com/dmw-phqd-bob
8)
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: https://meet.google.com/fng-adux-vyh