5 NOV 2025
17:30 - 19:00

Given an algebraic variety X defined by polynomial equations in several variables with coefficients in a field K, the most basic question is whether it has K-points, corresponding to solutions with K-coordinates of all these equations. In general, there are no solutions but unless the variety is empty, there are solutions which are defined over a finite extension L of K. We will then speak of L-points. The degree of a L-point is by definition the degree of the field extension L/K. The next important question is : what are the possible degrees of points of X? This question is more cohomological/Chow-theoretic in nature and we will discuss recent results in the case of del Pezzo surfaces and higher dimensional Fano varieties.

Venue: online
https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Website: http://math.ipm.ac.ir/agnt/
Venue: , (Online)

5 NOV 2025
14:00 - 15:00

در این سخنرانی، مسئله‌ای که توسط گابوریو (Gaboriau) مطرح شده و برای مدتی نسبتا طولانی باز بوده است را ثابت می‌کنیم. هزینه‌ یک گروه شمارای G ، به‌طور شهودی، کمینه‌ی �تعداد یال‌ها در واحد رأس� است که برای اتصال همه‌ عناصر G مورد نیاز است. منظور از اتصال، در نظر گرفتن یک گراف تصادفی همبند با رئوس G است به طوری که توزیع آن تحت عمل G ناوردا باشد. هزینه یک عملِ حافظ اندازه احتمال (pmp) از G نیز به طور مشابه تعریف می‌شود، با این شرط اضافه که گراف مورد نظر تابعی ناوردا و اندازه‌پذیر (یعنی یک فاکتور) از آن عمل باشد. یک گروه را دارای قیمت ثابت می‌گویند هرگاه تمام عمل‌های آزاد pmp آن هزینه برابر داشته باشند.
مسئله گابوریو این است که آیا حاصل‌ضرب مستقیم هر دو گروه شمارای نامتناهی، دارای قیمت ثابت یک است یا خیر. در مقاله اخیری توسط M. Fraczyk، S. Mellick و A. Wilkens که در دست چاپ در Annals of
Mathematics است، این موضوع برای ضرب درخت‌های منتظم و همچنین فضاهای متقارن رنک بالا ثابت شده است.

برای اثبات مساله برای ضرب دو گروه دلخواه، ابتدا خانواده‌ای تصادفی از گوی‌های بزرگ را در نظر می‌گیریم و نشان می‌دهیم که به یک فرآیند پواسون از کره‌های زمانی (horoball) میل می‌کند. سپس یک گراف به عنوان فاکتوری از این فرآیند می‌سازیم، به این صورت که ابتدا داخل هر کره زمانی یک جنگل با هزینه 1 می‌سازیم، و سپس یک نشت (percolation) با پارامتر خیلی کوچک به آن اضافه می‌کنیم. نشان می‌دهیم که، اگر رشد گروه مناسب باشد، داخل هر کره کاملا همبند می‌شود و هر دو کره زمانی نیز با افزودن نشت به یکدیگر مستقیما متصل می‌شوند، زیرا آن دو کره در نامتناهی جا با یکدیگر تماس دارند. به این ترتیب یک گراف همبند کم‌هزینه به دست می‌آوریم. در حالت رشد نامنظم گروه، حکم را با جایگزینی گوی‌ها با مجموعه‌های مناسب دیگر اثبات می کنیم.





Zoom room:

https://us06web.zoom.us/j/86247043799?pwd=KH1lKfYt1rGLzSgKk31MwprllTiOef.1


Meeting ID: 862 4704 3799


Passcode: 362880

Venue: Niavaran, Khosrovshahi Lecture Hall

5 NOV 2025
17:30 - 19:00

Periods are complex numbers defined by integrating algebraic differential forms over paths (on algebraic varieties) with algebraic end points. The set contains many interesting numbers like log 2 or π that have been studied intensely in transcendence theorem. By the linear version of the Period Conjecture (a theorem of Wustholz and myself in this case), all relations between them are described in terms of 1-motives. In this expository talk, we will explain this result and give a couple of examples.

Zoom link details:
Zoom link: https://kocun.zoom.us/j/99715471656
Meeting ID: 997 1547 1656
passcode: 848084
CS-File: https://researchseminars.org/seminar/FGC-IPM/ics
Venue: , (Online)

29 OCT 2025
16:00 - 17:00

Computers have been used to do calculations in mathematics for many decades. But in the last few years, several new ways to use computers to do mathematics have appeared. I'll give an overview of these ideas, explain where we are right now, and suggest where things might be going.
Venue: , (Zoom Lecture)

22 OCT 2025
17:30 - 19:00

Let X be a smooth variety over a field k, and let MBP^{iso} denote the isotropic motivic Brown-Peterson spectrum. In this talk, I will discuss the category of cellular MBP^{iso}-modules, also called isotropic Tate motives, over X. I will show how to endow this category with a motivic t-structure whose heart is Tannakian. This leads to the definition of a new invariant, called the isotropic motivic fundamental group of X. I will end with explicit computations for the punctured projective line and split tori.





Venue: online

https://zoom.us/join

Meeting ID: 9086116889

Passcode: 362880

Website: http://math.ipm.ac.ir/agnt/

22 OCT 2025
14:00 - 15:00

For given graphs ‎$G_1, G_2, ‎..., G_t‎$, the Ramsey number ‎$R(G_1, G_2, ‎..., G_t)‎$, is defined as the smallest positive integer ‎n‎ such that if the edges of ‎$K_n‎$ are partitioned into t disjoint color classes giving ‎$t‎$ graphs ‎$H_1, H_2, ‎..., H_t‎$, then at least one ‎H_i‎ has a sub-graph isomorphic to ‎G_i‎. The existence of such a positive integer is guaranteed by Ramsey's classical result. For ‎t>= ‎3‎‎, there is very little known about ‎‎$R(G_1, G_2, ‎..., G_t)‎$, even for some special graphs. In this talk, we consider the case that ‎‎$G_i‎‎‎$'s are either stars or matchings. The Ramsey number of matchings, was first studied by Cockayne and Lorimer and later, Burr and Roberts determined the Ramsey number for stars, showing a dependence on the parity of star sizes. Recently, Gyarfas and Sarkozy extended this to one star versus two matchings, answering a conjecture of Schelp. Here, we extend these results by determining the Ramsey numbers for any number of stars versus any number of matchings. In addition, we extend the result of Cockayne and Lorimer on the Ramsey number of matchings allowing host graphs with an Ore-type degree condition (a lower bound on the sum of the degrees of non-adjacent vertices). This result provides a far-reaching generalization of an important classical result of Erdos and Gallai and also giving a new proof for the graph case of the conjecture of Erdos dating back to 1965‎, known as the Erdos' matching conjecture.

Venue: Niavaran, Khosrovshahi Lecture Hall



Zoom room information:


https://us06web.zoom.us/j/86247043799?pwd=KH1lKfYt1rGLzSgKk31MwprllTiOef.1


Meeting ID: 862 4704 3799


Passcode: 362880

22 OCT 2025
17:30 - 19:00

The covering radius is an important parameter in coding theory. In this talk, we present several results concerning the covering radius of various classes of codes, obtained using techniques involving algebraic curves over finite fields. Connections to algebra, number theory, and geometry will also be discussed.

Zoom link details:
Zoom link: https://kocun.zoom.us/j/99715471656
Meeting ID: 997 1547 1656
passcode: 848084I
CS-File: https://researchseminars.org/seminar/FGC-IPM/ics
Venue: , (Online)