Speakers

  • Nezhla Aghaei
  • University of Hamburg
    Title: TBA
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    Nezhla Aghaei

    TBA

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  • Massoud Amini
  • Tarbiat Modares University
    Title: Programs in Mathematics
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    Massoud Amini

    This is a general review of some of the most famous Programs in Mathematics. We give a very short (and mainly historical) account of programs proposed by Riemann (1854) Klein (1872) Poincarè (1892) Hilbert (1900/1921) Weil (1949) Langlands (1967) Grothendieck (1984) Mori (1988). We also review some of the most famous classification programs, such as “Classification of von Neumann Algebras” (1936) “Classification of Finite Simple Groups” (1972) and “Classification of Separable Simple Nuclear Unital $C^{*}$-algebras” (1993). We give a short account of two programs proposed for the current century by Smale (1999) and Simon (2000).

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  • Farhad Babaee
  • University of Bristol
    Title: TBA
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    Farhad Babaee

    TBA

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  • Abdolnaser Bahlekeh
  • Gonbad Kavous University
    Title: Cohen-Macaulay artin algebras of finite Cohen-Macaulay type
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    Abdolnaser Bahlekeh

    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.

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  • Amir Farahmand Parsa
  • IPM
    Title: Kac-Moody groups, Dirac operators and discrete series representations
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    Amir Farahmand Parsa

    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.

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  • Ali Foroush Bastani
  • Institute for Advanced Studies in Basic Sciences
    Title: From option pricing theory to radial basis function approximation
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    Ali Foroush Bastani

    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.

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  • Mohammad Taghi Hajiaghaei
  • University of Maryland
    Title: TBA
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    Mohammad Taghi Hajiaghaei

    TBA

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  • Behnam Hashemi
  • Shiraz University of Technology
    Title: Numerical algorithms with automatic result verification: Recent advances in Chebyshev expansions and matrix functions
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    Behnam Hashemi

    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).

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  • Asma Hassannezhad
  • University of Bristol
    Title: A comparison between Steklov and Laplace eigenvalues on a Riemannian manifold.
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    Asma Hassannezhad

    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.

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  • Seyed Hamid Hassanzadeh
  • Federal University of Rio de Janeiro
    Title: Bounds on vector fields: degrees and generators
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    Seyed Hamid Hassanzadeh

    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

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  • Mehrdad Kalantar
  • University of Houston
    Title: Representation rigidity of subgroups and $C^\star$-algebras of quasi-regular representations
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    Mehrdad Kalantar

    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.

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  • Abbas Khalili
  • McGill University
    Title: Modeling heterogeneity of high-dimensional data: A finite mixture model approach
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    Abbas Khalili

    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

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  • Hashem Koohy
  • University of Oxford
    Title: Investigating mechanisms underlying the heterogeneity of response to caner immunotherapy by employing mathematical and machine-learning techniques
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    Hashem Koohy

    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.

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  • Sajjad Lakzian
  • IPM
    Title: Rigidity of spectral gap for non-negatively curved spaces
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    Sajjad Lakzian

    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).

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  • Behrooz Mirzaii
  • University of São Paulo
    Title: Bloch-Wigner Exact Sequence and Algebraic K-Theory
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    Behrooz Mirzaii

    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

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  • Maral Mostafazadeh Fard
  • Federal University of Rio de Janeiro
    Title: Divisor Class Group of Hankel Determinantal Rings
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    Maral Mostafazadeh Fard

    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 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

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  • Sam Nariman
  • Copenhagen/Purdue University
    Title: On obstructions to extending group actions to bordisms
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    Sam Nariman

    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.

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  • Azizeh Nozad
  • IPM
    Title: On Hodge-Euler Polynomials of Character Varieties
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    Azizeh Nozad

    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.

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  • Farzad Parvaresh
  • University of Isfahan
    Title: Coded Load Balancing in Cache Networks
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    Farzad Parvaresh

    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 Θ(log n) and Θ(log log 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.

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  • Massoud Pourmahdian
  • Amirkabir University of Technology & IPM
    Title: Probability: A logical viewpoint
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    Massoud Pourmahdian

    TBA

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  • Reza Rezaeian Farashahi
  • Isfahan University of Technology
    Title: TBA
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    Reza Rezaeian Farashahi

    TBA

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  • Arash Sadeghi
  • IPM
    Title: Vanishing of (CO)Homology over Local Rings
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    Arash Sadeghi

    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.

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  • Mohammad Safdari
  • Sharif University of Technology
    Title: Nonlinear elliptic equations with gradient constraints
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    Mohammad Safdari

    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 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.

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  • Amin Sakzad
  • Monash University
    Title: TBA
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    Amin Sakzad

    TBA

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  • Hadi Salmasian
  • University of Ottawa
    Title: Spherical superharmonics, singular Capelli operators, and the Dougall-Ramanujan identity
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    Hadi Salmasian

    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 Rep(O_t). This talk is based on joint work with Siddhartha Sahi and Vera Serganova.

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  • Maryam Shahsiah
  • University of Khansar
    Title: An Introduction to Ramsey Theory
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    Maryam Shahsiah

    TBA

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  • Farhad Shokoohi
  • University of Nevada Las Vegas
    Title: New Advances in Learning Finite Mixture of Regression Models with an Application in Cancer Research
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    Farhad Shokoohi

    There has been a growing demand for analysis of high-dimensional data subject to censoring and intangible heterogeneity of population, specifically in biology and health sciences. For instance, we may be interested in relationship between disease free time after surgery among ovarian cancer patients and their DNA methylation profiles of genomic features. Such studies pose additional challenges beyond the typical big data problem due to population substructure and censoring. In this talk, we first lay down the challenges arise due to the complex structure of high-dimensional data, and then we present our method to address some of these challenges. We specifically present the properties of our proposed method both theoretically and numerically. Finally, we analyze a dataset on high-grade serous ovarian cancer in an attempt to identify risky genes among over 9,000 genes. (This is a joint work with Professors Masoud Asgharian, Abbas Khalili and Shili Lin)

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  • Zahra Sinaei
  • University of Massachusetts Amherst
    Title: TBA
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    Zahra Sinaei

    TBA

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  • Majid Soleimani-Damaneh
  • University of Tehran
    Title: Some recent problems in vector optimization
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    Majid Soleimani-Damaneh

    The main aim of this presentation is to investigate some recent problems in multiobjective programming and vector optimization. To this end, ba- sic notions and approaches, including (weak/proper) eciency, scalarization, and compromise programming, are addressed. In addition to the required material from aforementioned elds, some preliminaries from nonsmooth op- timization are provided as well. Then, some recent topics around uncertainty, robustness, and di erentiability of the marginal mapping in vector optimiza- tion 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-di erentiability 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 devi- ation, Optimization 65 (2016) 1983-2005. [5] M. Rahimi, M. Soleimani-damaneh, Robustness in deterministic vector opti- mization, Journal of Optimization Theory and Applications, 179 (2018) 137-162.

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  • Reza Taleb
  • Shahid Beheshti University
    Title: Special values of Dedekind zeta-functions
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    Reza Taleb

    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.

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  • Pooya Vahidi Ferdowsi
  • Caltech
    Title: Classification of Choquet-Deny Groups
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    Pooya Vahidi Ferdowsi

    A countable discrete group is said to be Choquet-Deny if it has a trivial Poisson boundary for every non-degenerate probability measure on the group. In other words, a countable discrete group is Choquet-Deny if non-degenerate random walks on the group have trivial behavior at infinity. For example, all abelian groups are Choquet-Deny. It has been long known that all Choquet-Deny groups are amenable. I will present a recent result classifying countable discrete Choquet-Deny groups: a countable discrete group is Choquet-Deny if and only if none of its quotients have the infinite conjugacy class property. As a corollary, a finitely generated group is Choquet-Deny if and only if it is virtually nilpotent. This is a joint work with Joshua Frisch, Yair Hartman, and Omer Tamuz.

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  • Amirabbas Varshovi
  • University of Isfahan
    Title: Quantum Physics, Geometry and Topology
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    Amirabbas Varshovi

    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.

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  • Mehdi Yazdi
  • University of Oxford
    Title: The computational complexity of knot genus in a fixed 3-manifold
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    Mehdi Yazdi

    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.

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  • Hadi Zare
  • University of Tehran
    Title: On splitting Madsen-Tillmann spectra
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    Hadi Zare

    For a given compact Lie group G with an embedding of Lie groups G ---> 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

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