# Eventss

2019
May
01

# Analysis Seminar: Nir Lev (BIU) "On tiling the real line by translates of a function"

12:00pm to 1:00pm

## Location:

Ross 70

Title: On tiling the real line by translates of a function

Abstract: If f is a function on the real line, then a system

of translates of f is said to be a << tiling >> if it constitutes

a partition of unity. Which functions can tile the line by

translations, and what can be said about the structure of the

tiling? I will give some background on the problem and present

our results obtained in joint work with Mihail Kolountzakis.

Abstract: If f is a function on the real line, then a system

of translates of f is said to be a << tiling >> if it constitutes

a partition of unity. Which functions can tile the line by

translations, and what can be said about the structure of the

tiling? I will give some background on the problem and present

our results obtained in joint work with Mihail Kolountzakis.

2018
Jun
12

# T&G: Sara Tukachinsky (IAS), An enhanced quantum product and its associativity relation

1:00pm to 2:30pm

## Location:

Room 110, Manchester Buildling, Jerusalem, Israel

Open Gromov-Witten (OGW) invariants count pseudoholomorphic maps from a Riemann surface with boundary to a symplectic manifold, with constraints that make sure the moduli space of solutions is zero dimensional. In joint work with J. Solomon (2016-2017), we defined OGW invariants in genus zero under cohomological conditions. In this talk, also based on joint work with J. Solomon, I will describe a family of PDEs satisfied by the generating function of our invariants. We call this family the open WDVV equations.

2018
Jun
11

# HD-Combinatorics: Aner Shalev, "Probabilistically nilpotent groups"

10:00am to 10:50am

## Location:

Feldman Building, Givat Ram

In the past decades There has been considerable interest in the probability that two random elements of (finite or certain infinite)

groups commute.

I will describe new works (by myself and by others) on probabilistically nilpotent groups, namely groups in which the probability that [x_1,...,x_k]=1 is positive/bounded away from zero.

It turns out that, under some natural conditions,

these are exactly the groups which have a finite/bounded index

subgroup which is nilpotent of class < k.

The proofs have some combinatorial flavor.

groups commute.

I will describe new works (by myself and by others) on probabilistically nilpotent groups, namely groups in which the probability that [x_1,...,x_k]=1 is positive/bounded away from zero.

It turns out that, under some natural conditions,

these are exactly the groups which have a finite/bounded index

subgroup which is nilpotent of class < k.

The proofs have some combinatorial flavor.

2018
Jun
11

# HD-Combinatorics: Roy Meshulam, "Homology and Expansion of the spherical building"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram

Let X be the spherical building associated to the group G=GL(n,F) ,

where F is a finite field. We will survey some results on the homology of X with constant and twisted coefficients, and on the corresponding expansion properties.

where F is a finite field. We will survey some results on the homology of X with constant and twisted coefficients, and on the corresponding expansion properties.

2018
Jun
11

# HD-Combinatorics: Michael Chapman, "Conlon's construction of hypergraph expanders"

2:00pm to 3:50pm

## Location:

Feldman Building, Givat Ram

In this talk we recall Conlon's random construction of sparse 2-dim simplicial complexes arising from Cayley graphs of F_2^t . We check what expansion properties this construction has (and doesn't have): Mixing of random walks, Spectral gap of the 1-skeleton, Spectral gap of the links, Co-systolic expansion and the geometric overlap property.

2018
Jun
04

# HD-Combinatorics: Eli Shamir, "Almost optimal Boolean matrix multiplication[BMM] - By Multi-encoding of rows and columns"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram

Computing R=P.Q ,the product of two mXm Boolean matrices [BMM] is an ingredient

of many combinatorial algorithms.

Many efforts were made to speed it beyond the standard m^3 steps, without using

the algebraic multiplication.

To divide the computation task, encoding of the rows and column indices were

used (1.1) j by (j1,j2) k by (k1,k2)

e.g. using integer p j2=j mod p ,j1=ceiling of j/p.

Clearly, the product of the ranges of the digits= m1.m2 - is approximately m.

2018
Jun
04

# HD-Combinatorics: Shai Evra, "Gromov-Guth embedding complexity"

2:00pm to 3:50pm

## Location:

Feldman Building, Givat Ram

In this talk we shall review a paper by Gromov and Guth, in which they introduced several ways to measure the geometric complexity of an embedding of simplicial complexes to Euclidean spaces.

One such measurement is strongly related to the notion of high dimensional expanders introduced by Gromov, and in fact, it is based on a paper of Kolmogorov and Barzadin from 1967, in which the notion of an expander graph appeared implicitly.

We shall show one application of bounded degree high dimensional expanders, and present many more open questions arising from the above mentioned paper.

One such measurement is strongly related to the notion of high dimensional expanders introduced by Gromov, and in fact, it is based on a paper of Kolmogorov and Barzadin from 1967, in which the notion of an expander graph appeared implicitly.

We shall show one application of bounded degree high dimensional expanders, and present many more open questions arising from the above mentioned paper.

2018
Jun
04

# HD-Combinatorics: Prahladh Harsha, "Local Testability and Expansion"

10:00am to 10:50am

## Location:

Feldman Building, Givat Ram

Locally testable codes are error-correcting codes that admit

super-efficient checking procedures. In the first part of the talk, we will

see why expander based codes are NOT locally testable. This is in contrast

to typical "good" error correcting properties which follow from expansion.

We will then see that despite this disconnect between expansion and

testability, all known construction of locally testable codes follow from

the high-dimensional expansion property of a related complex leaving open

super-efficient checking procedures. In the first part of the talk, we will

see why expander based codes are NOT locally testable. This is in contrast

to typical "good" error correcting properties which follow from expansion.

We will then see that despite this disconnect between expansion and

testability, all known construction of locally testable codes follow from

the high-dimensional expansion property of a related complex leaving open

2018
Jun
06

# Eshnav : Dr. Chloé Perin : The shape of the universe

## Lecturer:

Dr. Chloé Perin

6:00pm to 7:15pm

## Location:

Manchester House, Lecture Hall 2, Hebrew University Safra Campus

##
**אשנב למתמטיקה : ד"ר קלואי פרין : הצורה של היקום**

יריעות הן מרחבים שנראים באופן מקומי כמו R

אנחנו נדבר על יריעות ממימד 2 (משטחים) ויריעות ממעמד 3, ועל דרכים בהן מתמטיקאים ניסו להבין איזה צורות יכולות להופיע.

נסביר את התוצאות העקריות בתחום: מיון המשטחים, והשערת הגיאומטריזציה של ת׳ורסטון, שהוכחה ע״י פרלמן ב 2003

^{n}(כמו למשל...היקום שלנו!), אבל הצורה הגלובלית שלהן יכולה להיות מאוד שונה מזו של R^{n}אנחנו נדבר על יריעות ממימד 2 (משטחים) ויריעות ממעמד 3, ועל דרכים בהן מתמטיקאים ניסו להבין איזה צורות יכולות להופיע.

נסביר את התוצאות העקריות בתחום: מיון המשטחים, והשערת הגיאומטריזציה של ת׳ורסטון, שהוכחה ע״י פרלמן ב 2003

2018
May
29

# Logic Seminar - Martin Goldstern - "Higher Random Reals"

1:30pm to 3:00pm

The set of real numbers is often identified with

Cantor Space 2^omega, with which it shares many important

properties: not only the cardinality, but also other

"cardinal characteristics" such as cov(null), the smallest

number of measure zero sets needed to cover the whole space,

and similarly cov(meager), where meager="first category";

or their "dual" versions non(meager) (the smallest

cardinality of a nonmeager set) and non(null).

Many ZFC results and consistency results (such as

Cantor Space 2^omega, with which it shares many important

properties: not only the cardinality, but also other

"cardinal characteristics" such as cov(null), the smallest

number of measure zero sets needed to cover the whole space,

and similarly cov(meager), where meager="first category";

or their "dual" versions non(meager) (the smallest

cardinality of a nonmeager set) and non(null).

Many ZFC results and consistency results (such as

2018
Jun
26

# Sieye Ryu (BGU): Predictability and Entropy for Actions of Amenable Groups and Non-amenable Groups

2:15pm to 3:15pm

Suppose that a countable group $G$ acts on a compact metric space $X$ and that $S \subset G$ is a semigroup not containing the identity of $G$. If every continuous function $f$ on $X$ is contained in the closed algebra generated by $\{sf : s \in S\}$, the action is said to be $S$-predictable.

In this talk, we consider the following question due to Hochman:

When $G$ is amenable, does $S$-predictability imply zero topological entropy?

To provide an affirmative answer, we introduce the notion of a random invariant order.

In this talk, we consider the following question due to Hochman:

When $G$ is amenable, does $S$-predictability imply zero topological entropy?

To provide an affirmative answer, we introduce the notion of a random invariant order.

2018
May
28

# HD-Combinatorics: Special Day on "Locally testable codes" (organized by Dorit Aharonov and Noga Ron-Zewi)

(All day)

## Location:

Eilat Hall, Feldman Building, Givat Ram

09:00 - 10:50

14:00 - 14:50

15:00 - 15:50

Abstract for Noga Ron-Zewi's talk:

**Noga Ron-Zewi**, "Locally testable codes"14:00 - 14:50

**Dorit Aharonov**, "Quantum error correcting codes"15:00 - 15:50

**Dorit Aharonov**, " Quantum Locally Testable codes and High dimensional expansion"Abstract for Noga Ron-Zewi's talk:

2018
Jun
07

2018
May
31

# Basic Notions: Mike Hochman - "Furstenberg's conjecture on transversality of semigroups and slices of fractal sets" Part I

4:00pm to 5:30pm

## Location:

Ross 70

In 1970, Furstenberg made a number of conjectures about the expansions of real numbers in non-comensurable bases, e.g. bases 2 and 3. The most difficult remains wide open, but several related problems, which can be stated in terms of the dimension theory of certain fractal sets, were recently settled. In the first talk I will try to describe the conjectures and some of what was known. In the second talk I will present Meng Wu's proof of the "slice conjecture" (it was also proved independently by Pablo Shmerkin, and I will try to also say a little about that proof too).