BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20241014T104500 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:9ae4939328b7cc8a2d9a0946f7786312 CATEGORIES:Symmetric Functions & Probability Theory Seminar CREATED:20251006T125347 SUMMARY:Subgroup Tests and the Aldous--Lyons Conjecture LOCATION:Hill 705 DESCRIPTION:The Aldous-Lyons Conjecture states that every (unimodular random rooted) in finite graph can be (Benjamini-Schramm) approximated by finite graphs. This conjecture is an analogue of other influential conjectures in mathematics concerning how well certain infinite objects can be approximated by finite ones; examples include Connes' embedding problem (CEP) in functional analys is and the soficity problem of Gromov-Weiss in group theory. These became m ajor open problems in their respective fields, as many other long standing open problems, that seem unrelated to any approximation property, were show n to be true for the class of finitely-approximated objects. For example, G ottschalk's conjecture and Kaplansky's direct finiteness conjecture are kno wn to be true for sofic groups, but are still wide open for general groups. \nIn 2019, Ji, Natarajan, Vidick, Wright and Yuen resolved CEP in the negat ive. Quite remarkably, their result is deduced from complexity theory, and specifically from undecidability in certain quantum interactive proof syste ms. Inspired by their work, we suggest a novel interactive proof system whi ch is related to the Aldous-Lyons conjecture in the following way: If the A ldous-Lyons conjecture was true, then every language in this interactive pr oof system is decidable. A key concept we introduce for this purpose is tha t of a Subgroup Test, which is our analogue of a Non-local Game. By providi ng a reduction from the Halting Problem to this new proof system, we refute the Aldous-Lyons Conjecture.\nThis talk is based on joint work with Lewis Bowen, Alex Lubotzky, and Thomas Vidick.\nNo special background in probabil ity theory, group theory, complexity theory or quantum information theory w ill be assumed.\n X-ALT-DESC;FMTTYPE=text/html:

The Aldous-Lyons Conjecture st ates that every (unimodular random rooted) infinite graph can be (Benjamini -Schramm) approximated by finite graphs. This conjecture is an analogue of other influential conjectures in mathematics concerning how well certain in finite objects can be approximated by finite ones; examples include Connes' embedding problem (CEP) in functional analysis and the soficity problem of Gromov-Weiss in group theory. These became major open problems in their re spective fields, as many other long standing open problems, that seem unrel ated to any approximation property, were shown to be true for the class of finitely-approximated objects. For example, Gottschalk's conjecture and Kap lansky's direct finiteness conjecture are known to be true for sofic groups , but are still wide open for general groups.

In 2019, Ji, Natarajan, Vidick, Wright and Yuen r esolved CEP in the negative. Quite remarkably, their result is deduced from complexity theory, and specifically from undecidability in certain quantum interactive proof systems. Inspired by their work, we suggest a novel inte ractive proof system which is related to the Aldous-Lyons conjecture in the following way: If the Aldous-Lyons conjecture was true, then every languag e in this interactive proof system is decidable. A key concept we introduce for this purpose is that of a Subgroup Test, which is our analogue of a No n-local Game. By providing a reduction from the Halting Problem to this new proof system, we refute the Aldous-Lyons Conjecture.

This talk is based on joint work with Lew is Bowen, Alex Lubotzky, and Thomas Vidick.

No special background in proba bility theory, group theory, complexity theory or quantum information theor y will be assumed.

CONTACT:Michael Chapman (IAS) DTSTAMP:20260830T041901 DTSTART;TZID=America/New_York:20251015T104500 DTEND;TZID=America/New_York:20251015T234500 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR