Previous Conferences & Workshops

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. ...

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...

The main source for the works of Archimedes is a medieval manuscript, written originally around in 975 CE and then erased and covered with a prayerbook in the year 1229. Briefly studied in 1906, the full contents of the manuscripts were finally...

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

Abstract: A central question in additive combinatorics is to determine what class of structured functions is enough to determine multilinear averages such as

$\mathbb{E}_{x,a} f_1(x) f_2(x+a) f_3(x+2a) f_4(x+3a)$.

In ergodic theory the analogous...

Abstract: In unpublished lecture notes, William A. Veech considered the following potential property of the Möbius function: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 respect...

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...

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...