BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Drupal iCal API//EN
X-WR-CALNAME:Events items teaser
X-WR-TIMEZONE:America/Toronto
BEGIN:VTIMEZONE
TZID:America/Toronto
X-LIC-LOCATION:America/Toronto
BEGIN:DAYLIGHT
TZNAME:EDT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
DTSTART:20250309T070000
END:DAYLIGHT
BEGIN:STANDARD
TZNAME:EST
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
DTSTART:20251102T060000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:69f57f2445743
DTSTART;TZID=America/Toronto:20260205T160000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20260205T172000
URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-214
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:KOSTIANTYN DRACH\, UNIVERSITAT DE BARCELONA\n\n_Reverse inradiu
 s inequalities for ball-bodies_\n\nA ball-body\, also called a $\\lambda$-
 convex body\, is an intersection\nof congruent Euclidean balls of radius $
 1/\\lambda$ in $\\mathbb{R}^n$\,\n$n \\geq 2$. Such bodies arise naturally
  in optimization problems in\ncombinatorial and convex geometry\, in parti
 cular when the number of\ngenerating balls is finite. In recent years\, ba
 ll-bodies have also\nplayed a central role in an active research program o
 n reverse\nisoperimetric-type problems under curvature constraints. The ge
 neral\nobjective of this program is to understand how prescribed curvature
 \nbounds restrict the extremal behavior of geometric functionals (e.g.\,\n
 volume\, surface area\, or mean width)\, and to identify sharp\ninequaliti
 es between them that reverse the existing classical\nisoperimetric-type in
 equalities. In this talk\, we focus on the\ninradius minimization problem 
 for $\\lambda$-convex bodies with\nprescribed surface area or prescribed m
 ean width. Here\, the inradius\nof a convex body $K$ is the radius of the 
 largest ball contained in\n$K$. In this setting\, we establish sharp lower
  bounds for the inradius\nand show that equality is attained only by lense
 s\, that is\,\nintersections of two balls of radius $1/\\lambda$. This sol
 ves a\nconjecture of Karoly Bezdek. We will outline the main ideas of the\
 nproof and pose several open problems. This is joint work with Kateryna\nT
 atarko.\n\nMC 5417
DTSTAMP:20260502T043548Z
END:VEVENT
END:VCALENDAR