Geometry
 & Topology 		IPM
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Graduate Course
Lecturers:
 Eaman Eftekhary & Meysam Nassiri
(School of Mathematics, IPM)
Title:
 Topology of Smooth Manifolds
Date: Thursdays, Fall 2018
Time: 8:30-10:00 & 10:30-12:00

(First lecture: Thursday, September 27, 2018, 8:30am)
Location: Lecture Hall 2,
Niavaran Building, IPM
Sh. Bahonar (Niavaran) Square, Tehran

Description:
This course is the first step in a one-year program, aimed at introducing topics in low dimensional topology and dynamical systems to starting graduate students and advanced undergraduates. The topics considered for the fisrt course include:
1- Smooth manifolds, Functions on manifolds, Sard theprem
2- Intersection theory and Thom theorem
3- Vector fields, Lefschetz fixed-point theorem
4- Differential forms, cohomology
5- Fundamental group, covering spaces and lifting lemmas
6- Homology groups
7- Morse theory

The program continues with topic courses on low dimensional topology and dynamical systems in the second semester (and possibly summer).

امکان ثبت نام رسمی در درس به عنوان دانشجوی مهمان در پژوهشکده ریاضیاتِ پژوهشگاه دانشهای بنیادی وجود دارد.

Problem Sets:


Lecture
Speakers:
 Salman Parsa
School of Mathematics, IPM
Title:

 An Algorithm for Contractability of Closed Curves on the Boundary of 3-manifolds
Description:

 The problem of deciding contractability of closed curves in a topological space is a fundamental problem in (computational) algebraic topology. In 3-manifolds, for simple curves on the boundary, the normal surface theory, as developed by Haken can be used to decide contractability. We present the first algorithm for this problem for closed curves on the boundary of 3-manifolds with self-intersections. The algorithm is based on the proof of the well-known Loop theorem and runs in exponential time.
Date &
Time:
 2018/12/19, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Mathematics Colloquium
Speakers:
 Thomas Fernique  (CNRS & Univ. Paris 13)
Title:

 Aperiodic Order
Description:

 We propose a wide-audience introduction to the notion of aperiodic order and its connections with numerous domain, as theoretical computer science, dynamical systems, combinatorics or discrete geometry, as well as motivations coming from condensed matter physics, namely quasicrystals. We shall in particular focus on aperiodic tilings characterized only by local constraints and bring a home-made aperiodic puzzle the audience can play with in order to better understand the concepts.
Date &
Time:
 2018/11/28, 16:00--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

8th Meeting on Contemporary Mathematics
School of Mathematics, IPM
June 19-20, 2018
Speaker:
 Danny Calegari
(University of Chicago)
Title:
 Surfaces and stable norms
Abstract:

Many fundamental geometric or topological problems can be couched in terms of finding a *simplest* representative of a given structure: a shortest path, a triangulation with fewest triangles, a least area surface. We discuss the theory of *stable commutator length*, ostensibly concerned with optimizing an algebraic quantity, and explain its relation to topology, geometry, and the homologically efficient construction of surfaces. There are many beautiful and unexpected phenomena. Some are understood; many more are not.
Program:

14:00-15:30
16:00-17:30
Tue
June 19
 1st Lecture Tea
 2nd Lecture
Wed
June 20
 3rd Lecture Tea Colloquium
+ reception

Location: Lecture Hall 1, IPM Niavaran Building,
Niavaran Square, Tehran
Registration:
 The attendance is free, but requires registration.
Please fill out the registration form and
send its text to  gt@ipm.ir  with the subject "MCM".
Poster

Mathematics Colloquium
Speakers:
 Danny Calegari
University of Chicago

Title:

 Ziggurats and Rotation Numbers
Description:

 The dynamical study of homeomorphisms of the circle is more than a century old; for a single homeomorphism Poincare found a beautiful invariant - the rotation number. In this talk we address the following fundamental question: if we know the rotation numbers of two homeomorphisms of the circle, what can we say about the rotation number of their product?
Date &
Time:
 Wednesday, Jun. 20, 2018, 16:00--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Tehran Topology 2018
School of Mathematics, IPM
June 26-28, 2018
Speakers: 
Mehrzad Ajoodanian (IPM)
Narges Bagherifard (Sharif Univ. Tech.)
Eaman Eftekhary (IPM)
Kristen Hendricks (Michigan State University)
Ali Kamalinejad (IPM)
Artem Kotelskiy (Princeton University)
Majid Narimannejad (IPM)
Meysam Nassiri (IPM)
Jacob Rasmussen (University of Cambridge)
Iman Setayesh (Tarbiat Modares University)
Mahdi Yazdi (University of Oxford) * (To be confirmed)
Hadi Zare (University of Tehran)
Organizers: 
Aliakbar Daemi (Stony Brook University & SCGP)
Eaman Eftekhary (IPM)
Robert Lipshitz (University of Oregon)
Faramarz Vafaee (Caltech)
Location: School of Mathematics, IPM,
Niavaran Square, Tehran
Registration:
 Please fill out the registration form and
send the text to gt@ipm.ir with the subject "TT2018".
Poster

Lecture
Speakers:
 Tahereh Aladpoosh
IPM
Title:

 On the Postulation of Scheme Theoretic Unions of Linear Subspaces of Projective Space
Description:

 A fundamental problem in Algebraic Geometry for projective schemes X is postulation problem. In fact to understand the geometry of X as an embedded scheme, one of the first points of interest is considering the postulation problem, i.e. determining the number of conditions imposed by asking hypersurfaces of any degree to contain X. There is an expected number of conditions- in this situation the scheme X is said to have good postulation. So a natural question to ask is: when does X have good postulation, and if it is not, why not? In the case when X is a scheme supported on unions of generic linear subspaces of a projective space there is much interest in this question because of many applications, and not only among algebraic geometers. This problem can be traced back to classical projective geometry, but the first complete result was achieved in 1981 by R. Hartshorne and A. Hirschowitz on the postulation of generic lines. After that, despite all the progress made on this problem, surprisingly very little is known about it, and the problem is still very live and widely open. In this talk we first introduce the postulation problem, then we discuss this problem for the scheme theoretic unions of linear spaces in projective space by giving main results and conjectures about them, and finally, we point out its connections with several research areas inside and outside of mathematics.
Date &
Time:
 2018/5/16, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

9th Meeting on Contemporary Mathematics
School of Mathematics, IPM
April 25-26, 2018
Speaker:
 Étienne Ghys
(École Normale Supérieure de Lyon)
Title:
 The topology of singular points of real analytic curves

Abstract:

In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ''analytic" chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

Program:

14:00-15:30
16:00-17:30
Wednesday
April 25
 1st Lecture Coffee Break
Colloquium
Thursday
April 26
 2nd Lecture Coffee Break 3rd Lecture

Location: Lecture Hall 1, IPM Niavaran Building,
Niavaran Square, Tehran
Registration:
 The attendance is free, but requires registration.
Please fill out the registration form and
send its text to  gt@ipm.ir  with the subject "MCM9".
Poster

Mathematics Colloquium
Speakers:
 Étienne Ghys
École Normale Supérieure de Lyon
Title:

 Traffic Jams: A Mathematical Problem?
Description:

 Traffic jams are nightmares in large cities. I would like to explain some mathematical ideas around the global dynamics of vehicles in complex networks. I will first show some paradoxes, like for instance the fact that it is sometimes a good idea to close a street in order to improve the traffic. Then I will describe some theorems which may not solve the problem, but which at least provide a better understanding of the phenomenon.
Date &
Time:
 Wednesday, April 25, 2018, 16:00--17:30
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Mohammad Reza Koushesh  (Isfahan University of Technology)
Title:

 Connectifying a Topological Space by Adding one Point
Description:

 In 1924, P. Alexandroff proved that a locally compact $T_2$-space has a $T_2$ one-point compactification (obtained by adding a ``point at infinity'') if and only if it is non-compact. He also asked for characterizations of spaces which have one-point connectifications. Here, we consider one-point connectifications, and in analogy with Alexandroff's theorem, we show that in the realm of $T_i$-spaces ($i=3\frac{1}{2},4,5$) a locally connected space has a one-point connectification if and only if it has no compact component. We explain how this theorem may be extended to the case $i=2$ and to the case $i=6$ under the set-theoretic assumption $\mathbf{MA}+\neg\mathbf{CH}$. Contrary to the case of the one-point compactification, a one-point connectification, if exists, may not be unique. We consider the collection of all one-point connectifications of a locally connected locally compact space in the realm of $T_i$-spaces ($i=3\frac{1}{2},4,5$). This collection, naturally partially ordered, is a compact conditionally complete lattice whose order-structure is rich enough to determine the topology of all Stone-Čech remainders of components of the space.
Date &
Time:
 2018/4/18, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Mohammad Javad Vanaei 
Tarbiat Modares University
Title:

 Cohomogeneity One Manifolds
Description:

 we present a review on the most symmetric non-homogeneous manifolds known as cohomogeneity one manifolds, i.e. pseudo-Riemannian $G$-manifolds where $G$ is a closed connected Lie subgroup of the isometry group and the lowest codimension of the orbits under the natural action of $G$ is one. Geometric and topological properties of such manifolds, their orbit spaces and orbit structures will be described and there will be a comparison between Riemannian and non-Riemannian $G$-manifolds to illustrate some basic differences.
Date &
Time:
 2018/4/11, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Solmaz Khajehpour
IPM
Title:

 Convexity on Riemannian Manifolds
Description:

 The significance of convexity in many areas of geometry is well- known; especially the solutions of some important PDEs, such as Abreu's and Monge-Amper equations, should be convex. In this lecture, by introducing some of the proximal calculus tools, I will talk about separation theorem for convex subsets of Riemannian manifolds. Moreover, I will explain why convexity of distance function $d_S$ to a closed convex subset $S$ of the Riemannian manifold with positive sectional curvature fails in some cases and by imposing some restriction on $S$, independently of curvature of M, the convexity of $d_S$ will be obtained.
Date &
Time:
 2018/2/7, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Hossein Mohadess
Amirkabir University of Technology
Title:

 Laplacian on Manifolds
Description:

 In the first part of the lecture, I describe some aspects of the spectral geometry related to the eigenvalues of the Laplace operator. In the second part, I talk about some results and problems in the case of lens spaces.
Date &
Time:
 2018/1/31, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Mathematics Colloquium
Speakers:
 Meysam Nassiri  (School of Mathematics, IPM)
Title:

 Topological Dynamics in Low Dimensions
Description:

 The dynamics of surface homeomorphism has witnessed a great development in recent years. Starting from some classical questions in dynamical systems, we will review the importance of the topological approach to the problems. In this talk, a central role is played by the remarkable concept of rotation number, introduced by H. Poincare a century ago.
Date &
Time:
 2018/1/24, 16:00--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Fatemeh Ghane
Ferdowsi University of Mashhad
Title:

 Skew Products and Invariant Graphs
Description:

 This talk concerns the stability and ergodic properties of skew products $T(x, y) =(f(x), g(x, y))$ in which $(f, X, \mu)$ is an ergodic map of compact metric space $X$ and $g : X \times Y \rightarrow Y$ is continuous. The set $X$ is the base, while $Y$ is the fiber. We consider the case where g is (non-uniformly) contracting. When this contraction is uniform, it can easily be shown that there exists a globally attracting invariant set which is the graph of a function from the base space to the fiber space. Here, we consider the case that the contraction rates are non-uniform and hence specifi ed by Lyapunov exponents and analogous quantities. We investigate the geometric structures of non-uniformly hyperbolic attractors of a certain class of skew products. We construct an open set of skew products over a linear expanding circle map such that any skew product belonging to this set admits a non-uniformly hyperbolic solenoidal attractor for which the following dichotomy is ascertained. This attractor is either a continuous invariant graph with nonempty interior or a thick bony attractor. Here, an attractor is, roughly speaking, a maximal attractor. Also, an attractor is thick if it has positive but not full Lebesgue measure. In our construction, the contraction in the fi ber is non-uniform. Furthermore, we provide some related results on the ergodic properties of attracting graphs and stability results for such graphs under deterministic perturbations. In particular, we show that there exists an invariant ergodic physical measure whose support is contained in that attractor.
Date &
Time:
 2018/1/17, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Farzad Fathizadeh
Swansea University, UK
Title:

 Arithmetic Structures in the Spectral Action of Bianchi IX Gravity Models
Description:

 In this talk, I will give a review of my recent joint works with Wentao Fan and Matilde Marcolli on a rationality phenomena and appearance of periods and motives in the heat kernel expansion of the Dirac-Laplacian of Bianchi IX gravity models with SU(2) symmetries. In the case of Bianchi IX gravitational instantons, which, in a succession of works by physicists and mathematicians, are characterized in terms of theta functions with characteristics, the terms in the expansion give rise to modular forms of weight 2, which we write explicitly in terms of Eisenstein series and the modular discriminant.
Date &
Time:
 2018/1/10, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

Lecture
Speakers:
 Hadi Zare
University of Tehran
Title:

 On Curtis Conjecture on Spherical Classes in $H_*QS^0$
Description:

 The problem of determining spherical classes in homology of spaces seems to be an elementary problem that one can stated once the Hurewicz map is defined. However, in some cases of interest such as the infinite loop space associated to the sphere spectrum, the answer still is unknown. In this talk, I will start with an introduction to spherical classes and their basic properties, and then state some recent developments in this direction which are obtained by geometric methods.
Date &
Time:
 2018/1/3, 15:30--17:00
Location: 
Lecture Hall 1,
IPM Niavaran Building,
Niavaran Square, Tehran
Printable Version

School of Mathematics,
IPM - Institute for Research in Fundamental Sciences
Niavaran Building, Niavaran Square, Tehran, Iran
Tel: +98 21 222 90 928
 Email: gt@ipm.ir