פעילויות השבוע
קולוקוויום
On face numbers of polytopes
יוני 18, 14:30—15:30, 2019, Math -101
מרצה
Eran Nevo (HUJI)
תקציר
A polytope is called simplicial if all its proper faces are simplices. The celebrated g-theorem gives a complete characterization of the possible face numbers (a.k.a. f-vector) of simplicial polytopes, conjectured by McMullen ’70 and proved by Billera-Lee (sufficiency) and by Stanley (necessity) ’80. The latter uses deep relations with commutative algebra and algebraic geometry. Moving to general polytopes, a finer information than the f-vector is given by the flag-f-vector, counting chains of faces according to their dimensions. Here much less is known, or even conjectured.
I will discuss what works and what breaks, at least conjecturally, when passing from simplicial to general polytopes, or subfamilies of interest.
AGNT
Number Theory in Function Fields.
יוני 19, 15:10—16:25, 2019, -101
מרצה
Lior Bary-Soroker (TAU)
תקציר
I will describe recent threads in the study of number theory in function fields, the different techniques that are used, the challenges, and if time permits the applications of the theory to other subjects such as probabilistic Galois theory.
BGU Probability and Ergodic Theory (PET) seminar
Maximum of exponential random variables and Hurwitz‘s zeta function
יוני 20, 11:10—12:00, 2019, -101
מרצה
Dina Barak (Ben-Gurion University)
תקציר
A problem, arising naturally in the context of the coupon collector‘s problem, is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al. (British J. of Math. & CS.:8 (2015), 330-336). Here we provide explicit asymptotic expressions for the moments of that maximum, as well as of the maximum of exponential random variables with the same parameters. We also deal with the probability of each of the variables being the maximal one.
The calculations lead to expressions involving Hurwitz‘s zeta function at certain special points. We find here explicitly the values of the function at these points.