IUT Mathematics Research Seminars (IMRS)

IUT Mathematics Research Seminars (IMRS)

About:  IMRS is a semi-periodic event which hosts single research or colloquium talks or series of talks about original research works as well as mini-courses and workshops, all from researchers working in various fields of Mathematics. This event is geared towards a more general audience. 

Youtube Channel

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:

Spring 2024:

Fall 2024:

Spring 2025:

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.

Venue: Kharazmi Conference Room, Department of Mathematics, IUT

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.

Venue: online

3)

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.

Venue: Kharazmi Conference Room, Department of Mathematics, IUT

4,5) (Minicourse)

Time: Wednesdays 4pm-4:50pm Tehran Time 

Dates: 

Session I : May. 8th, 2024 (19 Ordibehesht, 1403)
Session II : May. 15th, 2023 (26 Ordibehesht, 1403)
 

Speaker: Morteza Maleknia, Isfahan University of Technology

Title: First Steps in Optimization Theory

Abstract: Since the beginning of my work at IUT, I am almost daily faced with this question from students of various fields, most of whom are graduate students in engineering disciplines: ”Hello, Prof. Sorry, Do you have time?” ( yes, I have time). Prof. I need to solve an optimization problem in my research project. What is the best method (algorithm) for solving it?” In the first part of this course, we examine that this question is fundamentally meaningless, although it is not semantically meaningless! Then we learn how to properly analyze the different dimensions of an optimization problem and, consequently, how to correctly formulate our question and objective. In the second part, we delve into the concept that finding global minima of functions is equivalent to solving a wide range of problems in applied mathematics. Therefore, we must answer the question: Can we compute global minima for a general class of optimization problems, and if so, at what cost and using which algorithm? Participation in this short course does not require any specific prerequisites and is recommended for all undergraduate and graduate students, especially those in engineering fields.

Venue: Kharazmi Conference Room, Department of Mathematics, IUT

6) 

Date: September 23rd, 2024 (2 Mehr, 1403)

Time: Monday 3:00pm-5:00pm 

 Speaker: Amir Hashemi, Isfahan University of Technology

Title: On saturation of zero-dimensional ideals

Abstract: In this talk, I give first a brief review on a hidden algorithm due to Traverso in 1992 for computing Grobner bases. Specifically, it addresses the process of updating a  Grobner basis for a zero-dimensional ideal I to a Grobner basis for I+<f> where f is a new polynomial. This algorithm was formulated in one of Mora's books.  Based on this algorithm and by applying linear algebra techniques, we propose two new algorithms for calculating the saturation of a zero-dimensional ideal with respect to a polynomial. I will report  the efficiency of these methods compared to the classical method (using the Rabinowitsch trick) for computing ideal saturation. This talk is based on a joint work with my Ph.D. student; Fateme Akbari.

Venue: Kharazmi Conference Room, Department of Mathematics, IUT

7) 

Date: September 23rd, 2024 (2 Mehr, 1403)

Time: Monday 3:00pm-5:00pm 

 Speaker: Amin Talebi, Sharif University of Technology

Title: On saturation of zero-dimensional ideals

Abstract: ....

Venue: online

8) 

Date: Thursday, Nov. 14th, 2024 (24 Aban, 1403)

Time: 5:00pm-6:00pm Tehran Time (8:30am - 9:30am EST) 

 Speaker: Michael Munn, Google

Title: Leveraging implicit bias to improve efficiencies in training and fine-tuning ML models

Abstract:  In classical statistical learning theory, the bias variance trade off describes the relationship between the complexity of a model and the accuracy of its predictions on new data. In short, simpler models are preferable to more complex ones and, in practice, we often employ many techniques to control the model complexity. However, the best way to correctly measure the complexity of modern machine learning models remains an open question. In this talk, we will discuss the notion of geometric complexity and present some of our previous research which aims to address this fundamental problem. We'll also discuss current and future work which leverages this insight to devise strategies for more efficient model pre-training and fine-tuning.

Venue: online

9) 

Date: March 3rd, 2025 (13 Esfand 1403)

Time: Monday 4:00pm-5:00pm

 Speaker: Reza Mokhtari, Isfahan Univ. of Tech.

Title: Recent approaches to minimize condition numbers

Abstract:  In many applications, such as in the finite element method (FEM), the resulting linear system of equations has a coefficient matrix that is large and sparse with a very high condition number. As a result, utilizing some non-stationary methods like the conjugate gradient method (CGM) or its derivatives is too time-consuming to use the technique. One effective technique is to employ a suitable pre-conditioner before implementing the CGM or the preconditioned CGM (PCGM). However, constructing the pre-conditioner can be challenging in certain situations, such as when solving partial differential equations (PDEs). To address this issue, we intend to investigate the use of both optimization and deep neural network (DNN) approaches to construct suitable pre-conditioners for linear systems that arise from applying the FEM to solve some diffusion problems.

Venue: Kharazmi Conference Room, Department of Mathematics, IUT