# Mathematical INstitute @ Tel Aviv

## Coordinators

• Noga Alon
• Michael Krivelevich
• Leonid Polterovich

The Institute supports a variety of research-related activities at the School of Mathematical Sciences of TAU, including distinguished lectures, visitors, organization of workshops and travel of research students.

• Yakov Eliashberg (Stanford University)
• Peter Sarnak (Princeton University and IAS)
• Alain-Sol Sznitman (ETH, Zürich)

### Sergey Fomin (University of Michigan)

Date Day Time Location Title
2017-12-13 Wed 14:10 Schreiber 309 Morsifications and mutations
2017-12-18 Mon 12:15 Schreiber 006 Computing without subtracting (and/or dividing)

### Sergey Fomin (University of Michigan)

Date Day Time Location Title
2017-12-13 Wed 14:10 Schreiber 309 Morsifications and mutations
2017-12-18 Mon 12:15 Schreiber 006 Computing without subtracting (and/or dividing)

### Abstracts:

#### Morsifications and mutations

I will discuss a surprising connection between singularity theory and cluster algebras, more specifically between (1) the topology of isolated singularities of plane curves and (2) the mutation equivalence of the quivers associated with their morsifications. Joint work with Pavlo Pylyavskyy and Eugenii Shustin.

#### Computing without subtracting (and/or dividing)

Algebraic complexity of a rational function can be defined as the minimal number of arithmetic operations required to compute it. an restricting the set of allowed arithmetic operations dramatically increase the complexity of a given function (assuming it is still computable in the restricted model)? In particular, what can happen if we disallow subtraction and/or division? Joint work with Dima Grigoriev and Gleb Koshevoy.

### Benny Sudakov (ETH Zürich)

Date Day Time Location Title
2018-01-01 Mon 12:15 Schreiber 006 Rainbow structures, Latin squares & graph decompositions
2018-01-07 Sun 10:05 Schreiber 309 Unavoidable patterns in words

### Benny Sudakov (ETH Zürich)

Date Day Time Location Title
2018-01-01 Mon 12:15 Schreiber 006 Rainbow structures, Latin squares & graph decompositions
2018-01-07 Sun 10:05 Schreiber 309 Unavoidable patterns in words

### Abstracts:

#### Rainbow structures, Latin squares & graph decompositions

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs goes back to the work of Euler on Latin squares. Since then rainbow structures were the focus of extensive research and found applications in design theory and graph decompositions. In this talk we discuss how probabilistic reasoning can be used to attack several old problems in this area. In particular we show that well known conjectures of Ryser, Hahn, Ringel, and Graham-Sloane hold asymptotically.
Based on joint works with Alon, Montgomery, and Pokrovskiy.

#### TBA

A word $w$ is said to contain the pattern $P$ if there is a way to substitute a nonempty word for each letter in $P$ so that the resulting word is a subword of $w$. Bean, Ehrenfeucht and McNulty and, independently, Zimin proved Ramsey theorem for words. They characterised the patterns $P$ which are unavoidable, in the sense that any sufficiently long word over a fixed alphabet contains $P$. Zimin's characterisation says that a pattern is unavoidable if and only if it is contained in a Zimin word, where the Zimin words are defined by $Z_1 = x_1$ and $Z_n=Z_{n-1} x_n Z_{n-1}$.
We study the quantitative aspects of this theorem, showing that there are extremely long words (whose length is tower function) avoiding $Z_n$. Our results are asymptotically tight.
Joint work with David Conlon and Jacob Fox.