توجه : خانه رياضيات اصفهان هيچ نماينده‌ رسمي و شعبه ديگري ندارد. در صورت مشاهده چنين مواردي، درخواست مي‌شود تا از طريق تلفن 36692013 با خانه رياضيات اصفهان هماهنگ نمائيد.

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مدرسه بين‌المللي رياضي و کاشيکاري

 

آخرين مهلت ثبت‌نام : 31 فروردين 1394

لينک ثبت‌نام                 راهنماي ثبت‌نام 

مدرسه بين‌المللي رياضي و کاشي‌کاري

شهريور 1394، خانه رياضيات اصفهان
24 آگوست-4 سپتامبر 2015

آشنايي با  CIMPA 

CIMPA


 مدرسه بين‌المللي 10 روزه ریاضیات و علوم کامپیوتر برای شرکت دانش‌جويان ایران و کشورهای همسایه شهريور 1394 در شهر اصفهان برگزار خواهد شد. اين کارگاه به جنبه‌های ریاضی کاشی‌کاري در موارد مختلف، اختصاص داده شده و تلاش مي‌شود برنامه‌ها با انسجام بيشتري دنبال شود. برنامه‌هاي کارگاه به زبان انگليسي است.

 

  • هندسه گسسته (مدل سطوح گسسته)
  • محاسبه پذيري (محدودیت‌هایي که کاشی ‌کاري بتواند مدل اطلاعاتي انتقال اطلاعات را ارائه دهد، مشابه قوانین اتوماتاي سلولي)
  • احتمال (همگرایی فرایندهای تصادفی در کاشی کاری، به ویژه در نمونه گیری تصادفی و خواص نمونه‌ای از کاشی‌‌کاري‌های تصادفی)
  • ترکیبیات (شمارش تعداد روش‌هايي که مي‌توان منطقه‌اي را کاشی‌کاری نمود.)
  • ديناميک نمادین (برنامه‌نویسی مدارهاي سیستم‌های دینامیکی غیر دوره‌ای حداقل)
  • هندسه جبری موثر (استفاده از پایه گربنر برای بررسی قابليت کاشي‌کاري یک منطقه و یا وجود یک مشخصه از الگوهای محلی)

 علاوه بر موضوعات ذکر شده، سخنرانی‌های ماهواره‌ای مربوط به میراث غنی تاریخی اصفهان (و به طور کلی جهان اسلام)، که در آن کاشی‌کاري‌ها با تقارن شبه بلوری که اغلب در ساختمان معماری یافت می‌شود، نيز ارائه خواهد شد. خانه رياضيات  اصفهان در حال حاضر کارگاه‌های آموزشی را برگزار خواهد نمود.

کميته علمي :

كميته اجرايي :

Thomas Fernique : دانشگاه 13 پاريس
امير هاشمي : دانشگاه صنعتي اصفهان
رامين جوادي : دانشگاه صنعتي اصفهان
بهناز عمومي : دانشگاه صنعتي اصفهان
علي رجالي : دانشگاه صنعتي اصفهان و خانه رياضيات اصفهان

سخنرانان :


 

 

CIMPA

آشنايي با CIMPA

‍CIMPA كه مخفف (Centre International de Mathematiques Pures et Appliquees) به معني "مرکز همکاری‌های بین‌المللی ریاضیات محض و کاربردی" است و به منظور توسعه تحقیقات ریاضی در کشورهای در حال توسعه در سال 1978 میلادی در فرانسه تأسیس شد. این مرکز در شهر نیس واقع است و به عنوان یک مرکز رده 2 یونسکو شناخته می‌شود. هدف این مرکز ترویج آموزش و پژوهش در زمینه‌های ریاضیات بنیادی و کاربردی و همچنین در زمینه‌های مرتبط است. این مرکز با سازماندهی مدارس آموزشی و پژوهشی در زمینه‌های مذکور در یکی از کشورهای در حال توسعه زمینه‌های ارتباط علمی بیشتر بین آن کشور و کشورهای همسایه را فراهم می‌کند. لازم به ذکر است که سیمپا برای هر مدرسه با ارئه بورسیه‌هایی هزینه‌های مسافرت تعدادی از دانشجویان علاقمند از کشورهای همسایه را تامین می‌کند. تاکنون تعداد معدودی مدرسه تابستانی با همکاری سیمپا در ایران برگزار شده است که به عنوان نمونه به موارد زیر اشاره می‌کنیم :

الف- مدرسه پایه‌های گربنر و کاربردها در سال 2005 در زنجان  

ب- مدرسه نظریه نمایش جبرهادر سال 2008 در تهران

با همکاری سیمپا و دانشگاه پاریس 13 و خانه رياضيات اصفهان یک مدرسه تابستانی در زمینه ریاضیات و کشیکاری تحت عنوان "جورچینی و کاشیکاری" در شهریور 1394 در دانشکده علوم ریاضی دانشگاه صنعتی اصفهان برگزار خواهد شد که امیدواریم با مشارکت و استقبال قابل توجه دانشجویان مقاطع مختلف تحصیلی زمینه های همکاری علمی و رشد بیشتر دانشکده را فراهم کند. براي کسب اطلاعات بیشتر درباره سيمپا، اينجا را کليک نمائيد. 


Symbolic dynamics - Nicolas Bédaride

In this course we will consider symbolic dynamics. In a first part we will consider dynamics in dimension one by the action of the shift map over the sequences defined over a finite alphabet. We will consider several particular systems as Sturmian sequence, fixed point of substitutions, subshifts of finite type. Then in a second part we will consider systems in dimension two. They correspond to an action of Z² and are related to the tilings. For example the notion of subshifts of finite type can be defined and the Penrose tilings can be studied by this way

 

The dimer model in statistical mechanics  - Béatrice de Tillière

The goal of statistical mechanics is to study the large scale properties of a physics system, based on a probabilistic model describing microscopic interactions between components of the system. Many models belong to the field of statistical mechanics, as the Ising model, the percolation model, spanning trees and the dimer model. In these lectures, we shall focus on the dimer model, describing the adsorption of di-atomic molecules on the surface of a crystal. Equivalently, the dimer model has a representation as a tiling model. Our plan for these lectures is to - Explain the equivalence between the dimer model and the tiling model. Explain the interpretation of tilings, due to Thurston, as the projection of discrete surfaces. Prove the explicit formula, due to Kasteleyn and Temperley & Fisher, counting the number of dimer configurations of a finite, planar graph.  Introduce a probability measure on dimer configurations, and prove the explicit formula for it, due to Kenyon. Study the dimer model on infinite, bipartite, periodic graphs by giving a flavor of the paper ``Dimers and amoeba" by Kenyon, Okounkov and Sheffield. In this paper, the authors prove a full description of the model: they identify a two-parameter family of Gibbs measures, and give the full phase diagram using a deep connection to algebraic geometry

Self-assembly  - Eric Rémila

Self-assembly is the process by which small entities combine themselves into a bigger shape by local interactions in such a way that the resulting aggregates have interesting global properties. This framework consists in a refinement of Wang tiles, (i.e. side colored unit squares) where the colors of the sides are seen as different kinds of glues. These glues have different strengths which represent the strength of the affinity between the DNA sequences forming the sides of the tiles. Two equal glues will stick together, with a strength equal to the strength of the glues. The self-assembly of the tiles is controlled by the temperature, an integer T such that: a tile stays attached only if the sum of the strengths of the bonds with the other tiles along its sides is at least T, otherwise it is torn off from the rest of the crystal by thermal agitation. Some variations exist for the the modelization of the time (stochastic, parallel). During this lecture, we will investigate some complexity properties of this model. We will see how some families of shapes, or some tilings can be constructed by self-assembly, in an economic way. will also see some limits of the model

 

Cellular automata: a paradigm of complexity - Guillaume Theyssier

Like tilings, cellular automata are objects defined by simple local rules whose global behavior can be very complex in various ways. Contrary to tilings, the focus here is put on dynamics rather on geometry. We will make a tour of the rich mathematical theory of cellular automata, encountering on the way many important concepts such as: irreversibility, deterministic chaos, randomization, universality, phase transition, etc. While exposing the solid basis of what is known, we hope to show that a lot of exciting research perspectives remain in that field

 

Substitutive tilings - Chaim Goodman-Strauss

This lecture shall introduce the notions of substitution and cut & project tiling, which are two powerful tool to generate non-périodic tilings. We then focus on two important problems which were a great concern in tiling theory : Characterize the cut and project tilings which are substitutive and explicitly find a suitable substitution.  Prove that substitutive tilings admit matching rules, that is, are characterized by local constraints only.
Concrete examples shall be studied in details in tutorials

 

Flip dynamics  - Damien Regnault

This lecture focuses on flip, an elementary operation on rhombus tilings whose dynamics raises non trivial questions in combinatorics and probability. The first part of the lecture shall study the set of tilings of a given domain endowed with the flip operation: is it connected? can we bound the number of flips between two tilings? do we get some nice structure (e.g. a distributive lattice)? The second part of the lecture looks at the situation when probability comes into play: what do random flips on a tiling? in particular, we are interested in mixing time issues. The last part of the lecture mixes the previous questions with results of symbolic dynamics: what if the random flips are probabilized depending on their local environment? Can forbidden patterns be eventually removed? At which rate? We actually get close to statistical mechanics issues, with an original approach coming from symbolic dynamics. The underlying motivation is the growth of quasicrystals, seen here as aperiodic tilings.

 

Short lectures : 3h each

 

Order and symmetry of tilings - Thomas Fernique

This lecture aims to be an introduction to the core lectures of the school, in order to bring students with possibly very different background to a level which allows them to fully benefit from the school. We will thus introduce the notions of tilings, symmetry, calculability, probability, aperiodicity etc. which shall be further developed in the next lectures. We will also expose what makes the unity of the lectures of this school, which are the global motivations and the different approaches

 

Tilings in computer graphics and Islamic art  -Craig Kaplan

I will survey useful applications of tiling theory in computer graphics and digital design, with an emphasis on Islamic geometric patterns. After presenting some general techniques in algorithms and data structures for the representation and manipulation of tilings, I will take a tour through some interesting ways that tiling theory has been applied in computer graphics research. I will then focus on the generation of Islamic geometric patterns, and present a comprehensive suite of algorithms for creating and rendering patterns. I will also show how these ideas can easily be adapted from the Euclidean plane to the sphere, the hyperbolic plane, and arbitrary mesh surfaces

 

Effective algebraic geometry and tilings  - Amir Hashemi/Olivier Bodini

This course is an introduction to algebraic methods for finding tilability conditions. It requires nothing except some fondation of basic algebra. Firstly, we introduce the basic concept of Grobner Basis on the ring Z[X1, ...,Xn]. Grobner basis are used to algorithmically answer to the question of belonging of a polynomial to an ideal. The case of the ring Z [X1, ..., Xn] is less studied than conventional rings such as R[X1, ..., Xn] and C[X1, ..., Xn] and requires a little more attention. We then show how certain tilability conditions can be reduced to determining whether a polynomial associated to the region belongs to the ideal in Z[X1, ..., Xn] of polynomials associated to the set of tiles. In a final step, we will detail how to optimize some basic calculations of Grobner in the particular case of tilings

 

Enumeration and tilings   Frédérique Bassino

Given a region and a set of tiles, there are many different questions we can ask. The ones that we will address in this lecture are the following : - Is there a tiling ? - How many tilings are there exactly ?
- About how many tilings are there ? - What does a typical tiling looks like ? Examples we will consider include tilings by dominos, rectangles and squares.
Proofs are based on various combinatorial methods (bijections, analytic or algebraic combinatorics)

 

Satellite lectures

Tilings in contemporary architecture  - Jean-Marc Castera/Jay Bonner

Tilings in historical architecture  - Emil Makovicky/Jan P. Hogendijk

Tilings in physics  - Mohammad Taghi Tavassoli

Tilings and mathematical teaching - Akbar Zamani/Meghdad Ghari/Ali Rejali 

 

 

 

 CIMPA

 


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