Related Events

Time: JUL 22, 2017, 10:30 to 12:30
JUL 22, 2017, 14:00 to 16:00
JUL 23, 2017, 14:00 to 16:00
JUL 24, 2017, 10:30 to 12:30
JUL 24, 2017, 14:00 to 16:00

Venue: Lecture Hall 1, Niavaran Bldg., IPM

Abstract:
This course provides an introduction to the interactions between combinatorics and algebraic geometry, with an emphasize on combinatorial aspects of asymptotic Hodge theory.
The following topics will be covered:
1. Algebraic geometry of combinatorial objects
2. Differential geometry of polyhedral complexes
3. Combinatorial Hodge theory
4. Applications in combinatorics and algebraic geometry

Time: JUL 19, 2017, 14:00 to 15:30
JUL 19, 2017, 16:00 to 17:30

Venue: Lecture Hall 2, Niavaran Bldg., IPM

Abstract:
I will present an introduction to functions of bounded variation, 1-laplacian type equations, and least gradient problems. I shall discuss the applications of such problems to the inverse problem of recovering the electrical conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field. We will also consider this problem on electrical networks, i.e. the problem of determining the conductivity matrix of an electrical network from the induced current along the edges. I shall talk about the inverse problem of determining transition probabilities for random walks on graphs from the knowledge of the net number of times a random walker passes along the edges of the graph. The above problems hold potential for direct impact in medical imaging, analysis of computer and social networks, cryptography, and biology. At the same time, they lead to beautiful and challenging problems in analysis, geometric measure theory, weighted least gradient problems, theory of minimal surfaces, and numerical analysis.

Time: JUL 16, 2017, 11:00 to 12:30
JUL 16, 2017, 14:00 to 15:30

Venue: Lecture Hall 2, Niavaran Bldg., IPM

Abstract:
A major trend in non-commutative harmonic analysis is to investigate function spaces related to Fourier analysis (and representation theory) of non-abelian groups. The Fourier algebra and the Fourier-Steiltjes algebra, which are associated with the regular representation and the universal representation of the ambient group respectively, are important examples of such function spaces. These function algebras encode the properties of the group in various ways; for instance the non-existence of derivations on such algebras indicates their lack of analytic properties. In these lectures, we overview some important properties of these function algebras. For a locally compact group $G$, the Fourier-Stieltjes algebra of $G$, denoted by $B(G)$, is the set of all the matrix coefficient functions of $G$ equipped with pointwise algebra operations. Eymard proved that $B(G)$ can be identified with the dual of the group $C^*$-algebra of $G$. Moreover, the Fourier-Stieltjes algebra together with the norm from the above duality turns out to be a Banach algebra. We also study subspaces of $B(G)$, called $A_pi(G)$, generated by all the matrix coefficient functions of $G$ associated with a fixed unitary representation $\pi$. As an important example of such subspaces, we study the Rajchman algebra of $G$, denoted by $B_0(G)$, which is the set of elements of the Fourier-Stieltjes algebra that vanish at infinity.

Time: JUL 15, 2017, 11:00 to 12:30
JUL 15, 2017, 14:00 to 15:30

Venue: Room 221, Department of Mathematics,
Sharif University of Technology

Abstract:
The moduli space of a certain class of geometric objects parameterizes the isomorphism classes of such objects. Moduli spaces occur naturally in classification problems. They appear in many branches of mathematics and in particular in algebraic geometry. For a natural number $g > 1$ the moduli space $M_g$ classifies smooth projective curves of genus $g$. In 1961 Deligne and Mumford introduced a compactification of this space by means of stable curves. The geometry of these moduli spaces have been studied extensively since then by people from different perspectives. In this mini course we will give a review of well-known facts and conjectures about moduli spaces of curves and their invariants. Our main focus is on the study of the so called tautological classes on these moduli spaces in Chow and cohomology.

Time: JUL 15, 2017, 11:00 to 12:30
JUL 15, 2017, 14:00 to 15:30
JUL 15, 2017, 16:00 to 17:30

Venue: Lecture Hall 1, Niavaran Bldg., IPM

Abstract:
I will first give an introduction to the model theory of fields with valuations (for example the $p$-adic numbers), and the theory of $p$-adic and motivic integration. I will then consider the case of number fields, and present results on Dirichlet series and zeta functions which are Euler products of local integals, and give applications to some questions on algebraic groups, and rational points on algebraic varieties.

Time: JUL 10, 2017, 16:00 to 17:30

Venue: Lecture Hall 2, Niavaran Bldg., IPM

Abstract:
Given a graph $G=(V,E)$, a spanning forest $F$ is $\alpha$ thin with respect to $G$ if for any cut $(S,V-S)$, the number of edges of $F$ in the cut is at most $\alpha$ fraction of the number of edges of $G$. In this talk we will show that any $k$-edge connected graph $G$ has a $C/k$-thin forest with linear number of edges.

Time: JUL 10, 2017, 14:00 to 15:30

Venue: Lecture Hall 2, Niavaran Bldg., IPM

Abstract:
A multivariate polynomial is real stable if it has no roots in the upper half complex plane. These polynomials are recently used to resolve several long-standing open problems in mathematics and theoretical computer science. In this talk, we will see how these polynomials can be used to give a new proof of Van-der-Waerden conjecture. If time permits, I will discuss some applications in counting.

Time: JUL 9, 2017, 11:30 to 12:30
JUL 9, 2017, 14:00 to 15:00

Venue: Room 221, Department of Mathematics,
Sharif University of Technology

Abstract:
I will give two introductory lectures on the classification and representation theory of Lie superalgebras, and also the theory of symmetric functions, in particular the (shifted) Jack and Macdonald polynomials, and their super analogues defined by Sergeev and Veselov. The connections between the two theories is the solution to the ”Capelli eigenvalue problem”, which will be exhibited in my Frontiers conference lecture.

Time: JUL 9, 2017, 11:00 to 12:30
JUL 9, 2017, 14:00 to 15:30
JUL 9, 2017, 16:00 to 17:30

Venue: Lecture Hall 2, Niavaran Bldg., IPM

Abstract:
Many problems in probabilistic combinatorics can be formulated as the question of whether a randomly selected object in a given probability space falls outside a set of events (which we call "bad events"), with positive probability. When the events are pairwise independent, if the probability of each event is less than 1, then with positive probability, none of the events will occur. Unfortunately, in practice, the bad events are not always pairwise independent.
Lovasz Local Lemma (or LLL for short) asserts that if the bad events satisfy some weaker form of independence condition, then there exists a constant number $p$, independent of the number of the events, for which the following holds. If the probability of each bad event is less than $p$, then there exists a positive (although typically exponentially small) lower bound on the probability that none of them occur. Consequently, random sampling algorithm may take exponential time before it hits an object outside all the bad events.
In this short-course, we first motivate, explain by several examples and prove LLL. Then, we present the breakthrough work of Moser and Tardos about an algorithmic version of LLL which runs in polynomial time, in expectation.

Time: JUL 4, 2017, 10:00 to 12:30
JUL 4, 2017, 14:00 to 15:30
JUL 5, 2017, 10:00 to 12:30
JUL 5, 2017, 14:00 to 15:30
JUL 8, 2017, 10:00 to 12:30
JUL 8, 2017, 14:00 to 15:30

Venue: Room 221, Department of Mathematics,
Sharif University of Technology

Abstract:
Condensation is a widespread phenomenon that appears in various physical systems. From a mathematical point of view it can be seen as the spontaneous migration of a macroscopic number of particles to some region of the space. As a simple model I discuss the condensation phenomenon for a stochastic particle system known as Zero Range Process. In this system there is a one to one correspondence between condensates and metastable configurations. After a suitable time scaling, stochastic tunneling occurs and the system evolves among condensates.