# Special year - math workshop

Feb
27
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

10:00am
Sponsored by Dr. John P. Hempel

In person attendance is by invitation only.  All talks will by hybrid via Zoom.

Organizers: Mariusz Lemanczyk (IAS), Maksym Radziwill (Caltech), Tamar Ziegler (IAS)

Confirmed Speakers:
Teresa Anderson...

Feb
27
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Hardy-Littlewood and Chowla Type Conjectures in the Presence of a Siegel Zero
10:00am|Simonyi Hall 101 and Remote Access

Abstract: We discuss some consequences of the existence of a Siegel zero for various questions relating to the distribution of the prime numbers, and in particular to conjectures of Hardy-Littlewood and Chowla type.  This is joint work with Joni...

Feb
27
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

The Unipotent Mixing Conjecture
11:15am|Simonyi Hall 101 and Remote Access

Abstract: Low-lying horocycles are known to equidistribute on the modular curve. Here we consider the joint distribution of two low-lying horocycles of different speeds in the product of two modular curves and show equidistribution under certain...

Feb
27
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

On Random Polynomials and Counting Number Fields: Fourier Analysis Meets Arithmetic Statistics
Theresa Anderson
2:00pm|Simonyi Hall 101 and Remote Access

Abstract: Behaviors of objects of algebraic interest, such as polynomials, elliptic curves and number fields -- many of which are still unknown -- fall into the field of arithmetic statistics..  By bringing in Fourier analysis to interplay with a...

Feb
28
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Arbitrarily Slow Decay in the Mobius Disjointness Conjecture
10:00am|Simonyi Hall 101 and Remote Access

Abstract: We construct examples showing that the correlation in the Mobius disjointness conjecture can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of μ(n) one can put any bounded sequence such that...

Feb
28
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

On a Conjecture of Veech About Möbius Orthogonality
Thierry de la Rue
11:15am|Simonyi Hall 101 and Remote Access

Abstract: In unpublished lecture notes, William A. Veech considered the following potential property of the Möbius function:
"In any Furstenberg system of the Möbius function, the zero-coordinate is orthogonal to any function measurable with...

Feb
28
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Gowers Uniformity of Arithmetic Functions in Short Intervals
2:00pm|Simonyi Hall 101 and Remote Access

Abstract: I will present results establishing cancellation in short sums of arithmetic functions (in particular the von Mangoldt and divisor functions) twisted by polynomial exponential phases, or more general nilsequence phases. These results imply...

Mar
01
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Thermodynamic Formalism for B-free Dynamical Systems
Joana Kulaga-Przymus
10:00am|Simonyi Hall 101 and Remote Access

Abstract: Given $B \subset N$, we consider the corresponding set $FB$ of $B$-free integers, i.e. $n \in FB i_ no b \in B$ divides $n$. We $de_{ne} X \eta_}$ the B-free subshift _ as the smallest subshift containing $\eta := 1FB \in {0, 1}Z$. Such...

Mar
01
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Projection Theorems and Applications
11:15am|Simonyi Hall 101 and Remote Access

Abstract: Given a fractal set E in $R^n$ and a set F in $Gr(k,n)$, can we find k-plane S in F such that the orthogonal projection of E onto S is large?

We will survey some classical and recent projection theorems and discuss their applications. ...

Mar
01
2023

### Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Distribution of Orbits at Prime and Semi-prime Times
Abstract: For a topological dynamical systems (T, X) and a fixed $x \in X$ we are interested in the distribution of prime and semi-prime orbits, i.e. ${T px}p='$ and ${T p1p2 x}p1,p2='$. We are interested in systems for which the related sequences...