BEGIN:VCALENDAR
VERSION:2.0
CALSCALE:GREGORIAN
PRODID:iCalendar-Ruby
BEGIN:VEVENT
CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Speaker: Frederick Manners (UCSD)\n\nTitle: True Complexity
and iterated Cauchy-Schwarz arguments\n\nAbstract:\n\nLots of good things i
n combinatorics can be achieved by applying the Cauchy--Schwarz inequality
several times. For instance\, we know that if a graph has density $\alpha$
and $(1+o(1))\alpha^4 n^4$ 4-cycles then it has $(1+o(1)) \alpha^{15} n^{1
0}$ copies of the Petersen graph.\n\nOn the arithmetic side\, we know that
if a set $A \subseteq G$ has density $\alpha$ and no large non-trivial Four
ier coefficients\, it contains -- for instance -- $(1+o(1)) \alpha^3 |G|^2$
three-term progressions $x\,x+a\,x+2a$.\nBut does it also contain $(1+o(1)
) \alpha^6 |G|^3$ configurations\n\n$x\,x+z\,x+y\,x+y+z\,x+2y+3z\,2x+3y+6z$
\nor\n$x\,x+z\,x+y\,x+y+z\,x+2y+3z\,13x+12y+9z?$\n\nMoreover\, can you prov
e this by applying Cauchy--Schwarz multiple times? If so\, how do you find
such an argument\, and how horrifyingly long and complicated does it need
to be?\n\nWe will discuss some answers to these questions as well as some o
pen questions.
DTEND:20230303T210000Z
DTSTAMP:20241107T094621Z
DTSTART:20230303T200000Z
LOCATION:MIT-Math Dept.\, Room 2-139
SEQUENCE:0
SUMMARY:MIT-Harvard-MSR Combinatorics Seminar
UID:tag:localist.com\,2008:EventInstance_42547046953835
URL:https://calendar.mit.edu/event/mit-harvard-msr_combinatorics_seminar_16
67
END:VEVENT
END:VCALENDAR