## Speakers

 Nezhla Aghaei University of Hamburg Title: Heisenberg double and Drinfeld double of the quantumplane and super generalisations Abstract: view
 I start by the review of Hopf Algebra and explain how to find Heisenberg double and Drinfeld double algebra. I focus on Borel half of U_q(sl(2)) as an example and its relation with the theory of the deformations of the complex structures on Riemann surfaces. I will briefly explain the idea of the generalisation of this structure for the super algebra Osp(1|2). more details
 Farhad Babaee University of Bristol Title: Approximability of tropical currents Abstract: view
 Demailly in 2012 showed that the Hodge conjecture is equivalent to the statement that any $(p,p)$-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents; Moreover, the statement that all strongly positive currents with rational cohomology class can be approximated by positive linear combinations of integration currents, can be viewed as a strong version of the Hodge conjecture (1982). In this talk, I will explain a few basic notions in the theory of currents and in tropical geometry, and discuss how ideas from tropical geometry can be used to refute the latter statement. The talk is based on joint works with June Huh and Karim Adiprasito. more details
 Abdolnaser Bahlekeh Gonbad Kavous University Title: Cohen-Macaulay artin algebras of finite Cohen-Macaulay type Abstract: view
 The pure-semisimple conjecture predicts that every left pure-semisimple ring (a ring over which ev- ery left module is a direct sum of finitely generated ones) is of finite representation type. Left pure- semisimple rings are known to be left artinian by a result of Chase [6, Theorem 4.4]. The validity of the pure-semisimple conjecture for artin algebras comes from a famous result of Auslander [1] (also Ringel- Tachikawa [7]) where they have shown that an artin algebra $\Lambda$ is of finite representation type if and only if every left $\Lambda$-module is a direct sum of finitely generated modules. Recall that an artin algebra $\Lambda$ is of finite representation type, provided that the set of isomorphism classes of indecomposable finitely generated modules is finite. Inspired by Auslander's result, Chen [5] conjectured that Auslander-type result should be true for Gorenstein projective modules: an artin algebra $\Lambda$ is of finite Cohen-Macaulay type, in the sense that there are only finitely many isomorphism classes of indecomposable finitely generated Gorenstein projective $\Lambda$-modules, if and only if any left Gorenstein projective $\Lambda$-module is a direct sum of finitely generated modules. This conjecture has been answered affirmatively by Chen [5] for Gorenstein artin algberas, and by Beligiannis [4] for virtually Gorenstein artin algebras. In this talk, which is based on a joint work with Shokrollah Salarian and Fahimeh Sadat Fotouhi, we will examine the validity of this conjecture for Cohen-Macaulay artin algebras. This notion, which is a generalization of Gorenstein artin algebras, has been introduced by Auslander and Reiten; see [2, 3]. Recall that an artin algebra $\Lambda$ is said to be a Cohen-Macaulay algebra, if there is a $\Lambda$-bimodule $\omega$ such that the pair of adjoint functors $(\omega\otimes_{\Lambda}-,\hbox{Hom}_{\Lambda} (\omega,-))$ induces mutually inverse equivalences between the full subcategories of finitely generated $\Lambda$-modules, mod $\Lambda$, consisting of the $\Lambda$-modules of finite injective dimension and the $\Lambda$-modules of finite projective dimension. References [1] M. Auslander, A functorial approach to representation theory, in Representatios of Algebra, Workshop Notes of the Third Inter. Confer., Lecture Notes Math. 944, 105-179, Springer-Verlag, 1982. [2] M. Auslander and I. Reiten, Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), no. 1, 111-152. [3] M. Auslander and I. Reiten, Cohen-Macaulay and Gorenstein artin algebras, in Representation theory of finite groups and finite-dimensional algebras (Bielefeld 1991), Progress in mathematics, 95 (eds G. O. Michler and C. M. Ringel) (Birkhauser, Basel, 1991), pp.221-245. [4] A. Beligiannis, On algebras of finite Cohen-Macaulay type, Adv. Math. 226 (2011), no. 2, 1973-2019. [5] X. W. Chen, An Auslander-type result for Gorenstein projective modules, Adv. Math. 218 (2008), 2043-2050. [6] S. U. Chase, Direct product of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473. [7] C. M. Ringel and H. Tachikawa, QF-3 rings, J. Reine Angew. Math. 272 (1975), 49-72. more details
 Amir Farahmand Parsa IPM-Isfahan Title: Kac-Moody groups, Dirac operators and discrete series representations Abstract: view
 We will briefly introduce Kac-Moody groups as an infinite-dimensional generalization of Chevalley groups. Then by constructing Dirac-like operators, we will talk about possibility of integrating the notion of discrete series representations in this theory. more details
 Ali Foroush Bastani Institute for Advanced Studies in Basic Sciences Title: From option pricing theory to radial basis function approximation Abstract: view
 In this talk, I will start from a basic problem in computational finance, namely the ''American Option Pricing Problem'' by stating the problem and presenting a brief overview of the available approaches to tackle the problem. In the remainder, I will present an asymptotic-numeric approach to approximate the solution which will lead naturally to a class of radial basis functions widely used in the literature of multidimensional scattered data interpolation and approximation. By pointing to some possible research directions in this area, I will close the presentation. more details
 Behnam Hashemi Shiraz University of Technology Title: Numerical algorithms with automatic result verification: Recent advances in Chebyshev expansions and matrix functions Abstract: view
 Automatic result verification is a process that enables computers to obtain rigorous inclusions for the exact solution to a mathematical problem. While it uses floating point arithmetic to be fast, the results are guaranteed to be mathematically correct, even though rounding errors are almost everywhere in floating point arithmetic. Such algorithms have been successfully used in different applications, e.g., in computer-assisted proofs of important conjectures. We start with fundamentals of machine interval arithmetic involving directed roundings as defined in IEEE standard for floating point arithmetic. We then turn our attention to three specific problems and review a wide range of numerical algorithms with automatic result verification to tackle each problem. Specifically, we consider evaluation of Chebyshev expansions and computing matrix square roots and the matrix exponential. We close this talk with a quick review of challenges and open problems in this area. Parts of the work on Chebyshev expansions are done in collaboration with Jared Aurentz (Universidad Autonoma de Madrid, Spain), while results on the matrix square root and the matrix exponential are joint work with Andreas Frommer (University of Wuppertal, Germany). more details
 Asma Hassannezhad University of Bristol Title: A comparison between Steklov and Laplace eigenvalues on a Riemannian manifold. Abstract: view
 The Dirichlet-to-Neumann operator acts on smooth functions on the boundary of a Riemannian manifold and maps a function to the normal derivative of its harmonic extension. The eigenvalues of the Dirichlet-to-Neumann map are also called Steklov eigenvalues. It has been known that the geometry of the boundary has a strong influence on the Steklov eigenvalues. We show that for every $k\in N$ the $k$-th Steklov eigenvalue $\sigma_k$ is comparable to the square root of the $k$-th eigenvalue $\sqrt{\lambda_k}$ of the Laplacian on the boundary. Our results, in particular, give interesting geometric lower and upper bounds for Steklov eigenvalues. This is joint work with Bruno Colbois and Alexandre Girouard. more details
 Seyed Hamid Hassanzadeh Federal University of Rio de Janeiro Title: Bounds on vector fields: degrees and generators Abstract: view
 Finding algebraic integrals of a vector field is a fascinating question. Over a century ago Poincare had been interested in this question. Besides this fact, it is not clear what he might have asked about the algebraic integrals! The question of finding the minimum degree of a vector field which leaves a variety of invariant has had significant progress in the recent years. In this talk which is a report on ongoing work, we present a Commutative Algebraic point of view to the object. We show that the a-invariant of a ring is the numerical invariant that can unify and explain several previous results such as some in [Cerveau, Lins Neto, Esteves, Soares]. We determine lower bounds, upper bounds and bounds on the number of the generators of the module of non- trivial vector fields which leave a curve invariant. This is based on a joint work with: M. Chardin, C. Polini, A. Simis, and B. Ulrich more details
 Mehrdad Kalantar University of Houston Title: Representation rigidity of subgroups and $C^\star$-algebras of quasi-regular representations Abstract: view
 We introduce several equivalence relations on the set of subgroups of a countable group $G$, defined in terms of the quasi-regular representations, and present some rigidity results in terms of those equivalence relations for certain classes of subgroups. Furthermore, we give some results concerning the ideal structure of the $C^\star$-algebras generated by the quasi-regular representations. This is joint work with Bachir Bekka. more details
 Abbas Khalili McGill University Title: Modeling heterogeneity of high-dimensional data: A finite mixture model approach Abstract: view
 Latent variable models such as finite mixtures provide flexible tools for modeling data from heterogeneous populations consisting of multiple hidden homogeneous sub-populations. In this talk, I will review some of the recent methodological developments for estimation and feature selection problems in finite mixture of regression models, as a supervised learning approach, toward analyzing high-dimensional data more details
 Hashem Koohy University of Oxford Title: Investigating mechanisms underlying the heterogeneity of response to caner immunotherapy by employing mathematical and machine-learning techniques Abstract: view
 Personalized cancer immunotherapy is an area of cancer research that is gaining tremendous momentum. However, responses to immunotherapy are heterogeneous and patient care could be substantially improved by better understanding of how and why responses to immunotherapeutic approaches vary in different patients. Research interests in my group are focused on the development of machine-learning and computational approaches to help us further understand mechanisms underlying the heterogeneity of response to personalised cancer immunotherapy in which the patients’ immune system is modulated to find and kill cancer cells. more details
 Sajjad Lakzian Isfahan University of Technology and IPM-Isfahan Title: Rigidity of spectral gap for non-negatively curved spaces Abstract: view
 The first non-zero Neumann eigenvalue in a compact Riemannian manifold with non-negative Ricci curvature is larger than or equal to the squared of number $\pi$ divided by the square of the diameter of the space (this is sharp and is proven by Yang and Zhong '84). The rigidity result (proven by Hang and Wang '07) says the bound is achieved if and only if the underlying manifold is a circle or an interval. In this talk, I will discuss the proof of this rigidity result for all compact metric and measure spaces with non-negative weak Riemannian Ricci curvature (i.e. spaces with Ricci curvature bounds in the sense of Lott, Sturm and Villani that are infinitesimally Hilbertian in the sense of Ambrosio, Gigli and Savaré namely, posses Hilbert Sobolev space). These spaces in particular include Riemannian manifolds, Weighted manifolds, Alexandrov spaces, Ricci limit spaces and certain products, quotients and direct limits of such spaces. So our result proves the spectral gap rigidity for a very broad range of spaces including many singular ones. This is a recent joint work with C. Ketterer (University of Toronto) and Y. Kitabeppu (Kumamoto University). more details
 Behrooz Mirzaii University of São Paulo Title: Bloch-Wigner Exact Sequence and Algebraic K-Theory Abstract: view
 The Bloch-Wigner exact sequence appears in different areas of mathematics, such as Algebraic K-Theory, Three-dimensional Hyperbolic Geometry and Number Theory. In this talk I will introduce this exact sequence and give an application to Algebraic K-Theory. If time is left I will talk about its connection to other areas more details
 Maral Mostafazadeh Fard Federal University of Rio de Janeiro Title: Divisor Class Group of Hankel Determinantal Rings Abstract: view
 Hankel determinantal rings arise as homogeneous coordinate rings of higher order secant varieties of rational normal curves. In any characteristic we give an explicit description of divisor class groups of these rings and as a consequence we show that they are $\mathbb{Q}$-Gorenstein rings. It has been shown that each divisor class group element is the class of a maximal Cohen Macaulay module. Based on a joint work with Aldo Conca, Anurag K. Singh and Matteo Varbaro more details
 Sam Nariman Copenhagen/Purdue University Title: On obstructions to extending group actions to bordisms Abstract: view
 Motivated by a question of Ghys, we talk about cohomological obstructions to extending group actions on the boundary $\partial M$ of a $3$-manifold to a $C^0$-action on $M$. Among other results, we show that for a $3$-manifold $M$, the $S^1 \times S^1$ action on the boundary does not extend to a $C^0$-action of $S^1 \times S^1$ as a discrete group on $M$, except in the trivial case $M \cong D^2 \times S^1$. Using additional techniques from 3-manifold topology, homotopy theory, and low-dimensional dynamics, we find group actions on a torus and a sphere that are not nullbordant, i.e. they admit no extension to an action by diffeomorphisms on any manifold $M$ with $\partial M \cong T^2$ or $S^2$. This is a joint work with K.Mann. more details
 Azizeh Nozad IPM Title: On Hodge-Euler Polynomials of Character Varieties Abstract: view
 With the idea of symmetry, we can say that the presence and importance of the notion of groups and group actions (introduced by Galios and Lie) was realized in ancient times. Understanding of the quotient spaces turned out to be extremely useful both in algebraic and in geometric classification problems. These problems were greatly unified by the notion of moduli space, introduced by Riemann and developed by Mumford. In this talk we will introduce moduli spaces of representations of finitely presented group into a complex reductive Lie group, so called character varieties, and explain some techniques used in their study, mainly computations of more refined invariants such as Hodge-Euler polynomials. We will also give an overview of known explicit computations of these polynomials as well as some conjectures and present some open problems. more details
 Farzad Parvaresh University of Isfahan Title: Coded Load Balancing in Cache Networks Abstract: view
 We consider load balancing problem in a cache network consisting of storage-enabled servers forming a distributed content delivery scenario. Previously proposed load balancing solutions cannot perfectly balance out requests among servers, which is a critical issue in practical networks. Therefore, we investigate a coded cache content placement where coded chunks of original files are stored in servers based on the files popularity distribution. In our scheme, upon each request arrival at the delivery phase, by dispatching enough coded chunks to the request origin from the nearest servers, the requested file can be decoded. Here, we show that if $n$ requests arrive randomly at $n$ servers, the proposed scheme results in the maximum load of $O(1)$ in the network. This result is shown to be valid under various assumptions for the underlying network topology. Our results should be compared to the maximum load of two baseline schemes, namely, nearest replica and power of two choices strategies, which are $\Theta(\text{log}\hspace{2pt}n)$ and $\Theta(\text{log}\hspace{2pt}\text{log}\hspace{2pt}n),$ respectively. This finding shows that using coding, results in a considerable load balancing performance improvement, without compromising communications cost performance. This is confirmed by performing extensive simulation results, in non-asymptotic regimes as well. more details
 Massoud Pourmahdian Amirkabir University of Technology & IPM Title: Probability: A logical viewpoint Abstract: view
 In this talk I will review various logical aspects of probability, in particular, introducing some extensions of propositional and first-order logics relevant for probabilistic reasoning. If time permits, I will also discuss some logical aspects of random graphs. more details
 Reza Rezaeian Farashahi Isfahan University of Technology Title: Applications of Elliptic curves Abstract: view
 Elliptic curves have received a lot of attention throughout the past 4 decades. They have been playing an increasingly important role both in number theory and in related fields such as cryptography. For example, they were used in the proof of Fermat's Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization. In this talk, we review some applications of elliptic curves in number theory and modern public-key cryptography. more details
 Arash Sadeghi IPM Title: Vanishing of (CO)Homology over Local Rings Abstract: view
 In this talk, we will discuss about the vanishing of (co)homology over commutative Noetherian local rings. A remarkable consequence of the vanishing of homology is the depth formula, $\text{depth}_{R}(M)+\text{depth}_{R}(N) = \text{depth}(R)+\text{depth}_{R}(M\otimes_{R}N),$ established by Auslander when $R$ is regular. In the first part of this talk, we will discuss about the depth formula over Gorenstein rings. In the second part, we will talk about Auslander–Reiten Conjecture. This is one of the most celebrated conjectures in the representation theory of algebras. We will present various criteria for freeness of modules over local rings in terms of vanishing of cohomology, which recover a lot of known results on the Auslander–Reiten Conjecture. more details
 Mohammad Safdari Sharif University of Technology Title: Nonlinear elliptic equations with gradient constraints Abstract: view
 We consider nonlinear elliptic equations with gradient constraints, which arise from both variational and non-variational formulations. Equations of this type appear in the theory of elasticity, the study of random surfaces, or stem from dynamic programming in many stochastic singular control problems. We do not assume any regularity about the constraints; so the constraints need not be C1 or strictly convex. We will show that the solution to these problems have the optimal W2,∞ regularity. more details
 Amin Sakzad Monash University Title: Middle-Product Learning with Errors Abstract: view
 We introduce a new variant MP-LWE of the Learning With Errors problem (LWE) making use of the Middle Product between polynomials modulo an integer $q$. We exhibit a reduction from the Polynomial-LWE problem (PLWE) parametrized by a polynomial $f$, to MP-LWE which is defined independently of any such $f$. The reduction only requires $f$ to be monic with constant coefficient coprime with $q$. It incurs a noise growth proportional to the so-called expansion factor of $f$. We also explore some applications of different variants of MPLWE. more details
 Hadi Salmasian University of Ottawa Title: Spherical superharmonics, singular Capelli operators, and the Dougall-Ramanujan identity Abstract: view
 Abstract : Given a multiplicity-free action $V$ of a simple Lie (super)algebra $g$, one can define a distinguished "Capelli" basis for the algebra of $g$-invariant differential operators on $V$. The problem of computing the eigenvalues of this basis was first proposed by Kostant and Sahi, and has led to the theory of interpolation polynomials and their generalizations. In this talk, we consider an example associated to the orthosymplectic Lie superalgebras, which leads to "singular" Capelli operators, and we obtain two formulas for their eigenvalues. Along the way, the Dougall-Ramanujan identity appears in an unexpected fashion. If time permits, we will transcend some of our results to theorems in Deligne's category $\text{Rep}(O_t).$ This talk is based on joint work with Siddhartha Sahi and Vera Serganova. more details
 Maryam Shahsiah University of Khansar Title: An Introduction to Ramsey Theory Abstract: view
 Ramsey theory refers to a large body of deep results in mathematics whose underlying philosophy is captured succinctly by the statement that \every large system contains a large well-organized subsystem." This is an area in which a great variety of techniques from many branches of mathematics are used and whose results are important not only to graph theory and combinatorics but also to logic, analysis, number theory, and geometry. The cornerstone of this area is Ramsey's theorem, which guarantees the existence of Ramsey numbers. De- termining or estimating Ramsey numbers is one of the central problems in combinatorics. Besides the complete graph, the next most classical topic in this area concerns the Ramsey numbers of sparse graphs, i.e., graphs with certain upper bound constraints on the degrees of the vertices. One can naturally try to extend the sparse graph Ramsey results to hyper- graphs. In this talk, we present some obtained results on Ramsey number of sparse graphs and hypergraphs. We speci cally present the relevant results on Ramsey number of loose cycles. more details
 Zahra Sinaei University of Massachusetts Amherst Title: Convex functional and the stratification of the singular set of their stationary points Abstract: view
 In this talk, I discuss partial regularity of stationary solutions and minimizers $u$ from a set $\Omega\subset \hspace{2pt}\mathbb{R}^n$ to a Riemannian manifold $N$, for the functional $\int_\Omega F(x,u,|\nabla u|^2) dx.$ The integrand $F$ is convex and satisfies some ellipticity, boundedness and integrability assumptions. Using the idea of quantitative stratification I show that the $k$-th strata of the singular set of such solutions are $k$-rectifiable. more details
 Majid Soleimani-Damaneh University of Tehran Title: Some recent problems in vector optimization Abstract: view
 The main aim of this presentation is to investigate some recent problems in multi-objective programming and vector optimization. To this end, basic notions and approaches, including (weak/proper) efficiency, scalarization, and compromise programming, are addressed. In addition to the required material from aforementioned fields, some preliminaries from nonsmooth optimization are provided as well. Then, some recent topics around uncertainty, robustness, and differentiability of the marginal mapping in vector optimization are discussed. This presentation is based some works joint with L. Pourkarimi (Razi University), M. Rahimi (University of Tehran), D.T. Luc (Avignon University), and M. Zamani (Ferdowsi University). Main References: [1] F. Clarke, Functional analysis, calculus of variations and optimal control. Springer-Verlag, London, 2013. [2] M. Ehrgott, Multicriteria optimization. Springer, Berlin, 2005. [3] D.T. Luc, M. Soleimani-damaneh, M. Zamani, Semi-differentiability of the marginal mapping in vector optimization, SIAM Journal on Optimization, 28 (2018) 1255-1281. [4] L. Pourkarimi, M. Soleimani-damaneh, Robustness in deterministic multiple objective linear programming with respect to the relative interior and angle deviation, Optimization 65 (2016) 1983-2005. [5] M. Rahimi, M. Soleimani-damaneh, Robustness in deterministic vector optimization, Journal of Optimization Theory and Applications, 179 (2018) 137-162. more details
 Reza Taleb Shahid Beheshti University Title: Special values of Dedekind zeta-functions Abstract: view
 For a number field $F$ and an integer $n \geq 2$, the special values $\zeta_{F}(1-n)$ of Dedekind zeta-function $\zeta_{F}(s)$ at $s = 1-n$ are closely related to certain algebraic $K$-groups and motivic cohomology groups by some conjectures, e.g. Lichtenbaum conjecture and Coates- Sinnott conjecture. In this talk after giving the definitions and formulations we survey the relevant results on these conjectures. more details
 Amirabbas Varshovi University of Isfahan Title: Quantum Physics, Geometry and Topology Abstract: view
 We have a brief review over special topics of topological and geometric aspects of quantum field theories. First we argue about Atiyah-Singer index theorem, Chern-Weil characters, Hirzebrugh and Dirac indices, and then we introduce the gauge and gravitational anomalies in quantum field theories by means of introduced topological invariants. Finally, we try to give topological intuitions about the meaning of given formulas. more details
 Mehdi Yazdi University of Oxford Title: The computational complexity of knot genus in a fixed 3-manifold Abstract: view
 The genus of a knot in a 3-manifold is defined to be the minimum genus of a compact, orientable surface bounding that knot, if such a surface exists. In particular a knot can be untangled if and only if it has genus zero. We consider the computational complexity of determining knot genus. Such problems have been studied by several mathematicians; among them are the seminal works of Hass-Lagarias-Pippenger, Agol-Hass-Thurston, Agol and Lackenby. For a fixed 3-manifold the knot genus problem asks, given a knot K and an integer g, whether the genus of K is equal to g. Marc Lackenby proved that the knot genus problem for the 3-sphere lies in NP. In joint work with Lackenby, we prove that this can be generalised to any fixed, compact, orientable 3-manifold, answering a question of Agol-Hass-Thurston from 2002. more details
 Hadi Zare University of Tehran Title: On splitting Madsen-Tillmann spectra Abstract: view
 For a given compact Lie group $G$ with an embedding of Lie groups $G\hookrightarrow O(n)$ one can associate a Thom spectrum, known as a Madsen-Tillman spectrum, $MTG=BG^{-\gamma}$ where $\gamma$ is the pull back of the universal bundle over $BO(n)$. We show that upon choosing suitable compact subgroups $H\leq G$ then $MTH$ splits off $MTG$. We also hint on some recent results on splitting $MTO(n)$ using Steinberg idempotents. These results are based on joint work with Takuji Kashiwabara. more details