Конференция $А.М. ≥ 50$ в честь юбилея А.М. Райгородского в МФТИ

13 - 14 июля, 2026
Долгопрудный
МФТИ
13 - 14 июля 2026 в МФТИ пройдет небольшая комбинаторная конференция $A.M.≥50$, посвященная 50-летию Андрея Михайловича Райгородского.

Пленарные докладчики

Imre Bárány Rényi Institute of Mathematics, Hungary Stefano Boccaletti Institute for Complex Systems, Italy Gyula O. H. Katona Rényi Institute of Mathematics, Hungary János Pach Rényi Institute of Mathematics, Hungary Герман Олег Николаевич НИУ ВШЭ
Долбилин Николай Петрович Математический интститут им. В.А. Стеклова РАН Кабатянский Григорий Анатольевич МФТИ Карасёв Роман Николаевич МФТИ Мощевитин Николай Германович МГУ Семенов Алексей Львович НИУ ВШЭ

Секционные докладчики

Воронов Всеволод Александрович МФТИ Жуковский Максим Евгеньевич МФТИ, University of Sheffield, UK Купавский Андрей Борисович МФТИ
Носков Федор Андреевич МФТИ Шубин Яков Константинович МФТИ И другие

Расписание

Here is the schedule of conference talks for November 26 and 27. There also will be an additional lecture by Gábor Tardos (November 28) and two lectures by István Tomon (November 29 and December 2), follow the links for more details.
13 июля
9.40 - 10.30
Roman Karasev
Envy-free divisions and mapping degrees
joint work with Sergey Avvakumov, Arkadiy Skopenkov, and Sergey Kudrya
Room: 424 Arctica

We discuss some classical problems of mathematical economics, in particular, so-called envy-free division problems. The classical approach to some of such problems reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster–Kuratowski–Mazurkiewicz theorem and the Gale theorem) is a boundary condition.

We try to replace the boundary condition by a certain equivariance condition under all permutations, or a weaker condition of "pseudo-equivariance'', which has a certain real-life meaning for the problem of partitioning a segment and distributing the parts among the players. It turns out that we can guarantee the existence of a solution for the segment partition problem when the number of players is a prime power; and we may produce instances of the problem without a solution otherwise. The case of three players was solved previously by Segal–Halevi, the prime case and the case of four players were solved by Meunier and Zerbib.

Going back to the true equivariance setting, we provide, in the case when the number of players is not a prime power and not twice a prime power, the counterexamples showing that the topological configuration space / test map scheme for a wide class of equipartition problems fails and some envy-free division problems have a counterexample. Moreover, this is also applicable to building stronger counterexamples for the topological Tverberg conjecture.

12.00 - 14.20
Lunch
15.30 - 16.00
Coffee Break
Room: Lecture Hall 4th floor Arctica
14 июля
9.40 - 10.30
János Pach
Strings and Order
Room: 119 Main Building

Let $\omega(G)$ and $\chi(G)$ denote the clique number and chromatic number of a graph $G$, respectively. The disjointness graph of a family of curves (continuous arcs in the plane) is the graph whose vertices correspond to the curves and in which two vertices are joined by an edge if and only if the corresponding curves are disjoint. A curve is called $x$-monotone if every vertical line intersects it in at most one point.

We solve a 25 years old problem by showing that for arbitrarily large integers $k$, there exist families of $x$-monotone curves such that their disjointness graphs $G$ satisfy $\omega(G)=k$ and $\chi(G)=\Omega(k^4)$. This bound is asymptotically tight.

If we drop the condition that the curves are $x$-monotone, then $\chi(G)$ cannot be bounded in terms of $k$. We construct, for every $g>3$, families of $n$ curves such that the girth of their disjointness graphs $G$ is at least $g$ and $\chi(G)=\Omega_g(\log n)$. This improves a result of Bollobás. Joint work with István Tomon.

11.30 - 14.00
Lunch
15.30 - 16.00
Coffee Break
Room: Lecture Hall 4th floor Arctica

Локация

Конференция пройдет в Физтех.Клубе, г. Долгопрудный, Первомайская 3А, ТЦ Дирижабль, 2 этаж (ссылка на Яндекс.Карту).

Мы будем рады всем гостям конференции! Если вы не являетесь студентом или сотрудником МФТИ, не забудьте взять с собой паспорт.

Из Москвы на электричке большого диаметра D1
Добираться из Москвы до станции "Новодачная" удобнее всего поездами цетрального диаметра D1. Конкретный маршрут можно проложить на интерактивной карте метро (выберите станцию "Новодачная" как точку назначения).
На такси
Для быстрого заказа такси приведем ссылку на сервис Яндекс.Такси (он также доступен по телефону +7 (495) 999 99 99).