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:20211107T010000 RDATE:20220313T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20221106T010000 RDATE:20230312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20231105T010000 RDATE:20240310T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD 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:20210329T153000 RDATE:20211107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20220313T030000 RDATE:20221106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20230312T030000 RDATE:20231105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20240310T030000 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:f1cd5a147f6087e8f4fc265405ea9093 CATEGORIES:Colloquia CREATED:20220324T095739 SUMMARY:Tiling problems, old and new LOCATION:Zoom DESCRIPTION:Abstract: A classic puzzle is to show that an 8-by-8 square cannot be tiled by 1-by-2 and 2-by-1 rectangles if two opposite 1-by-1 corner-squares are removed. A less famous puzzle is to count how many tilings there are if you DON’T remove those corners. This is an example of a dimer problem, first c onsidered by physicists, at the intersection of graph theory and enumerativ e combinatorics. I’ll review some highlights in the theory of dimers, displ aying elegant formulas for the number of tilings and striking pictures of t he kinds of long-range order that can arise spontaneously. \nThen I’ll disc uss beautiful work of Conway, Lagarias, and Thurston applying combinatorial group theory to the study of tiling problems, yielding criteria for distin guishing between doable and non-doable tiling problems. I’ll apply the meth od to obtain a surprising result about a class of tiling problems that are ALMOST never doable.\nFinally, bringing the two strands together, I’ll disc uss my recent empirical work counting tilings related to trimer models. Non e of the methods that I know of for obtaining exact formulas for dimers app ly here, yet the data show a wealth of patterns suggesting that there are d eep theorems to be proved. Especially mysterious are some patterns involvin g the 2-adic numbers.\nThis talk should be understandable to undergraduates . No background in graph theory, enumerative combinatorics, combinatorial g roup theory, or p-adic analysis will be required, and you won’t need to kno w what a dimer or a trimer is when you arrive (though you will when you lea ve).\n X-ALT-DESC;FMTTYPE=text/html:

Abstract: A classic puzzle is to show that an 8-by-8 square cannot be ti led by 1-by-2 and 2-by-1 rectangles if two opposite 1-by-1 corner-squares a re removed. A less famous puzzle is to count how many tilings there are if you DON’T remove those corners. This is an example of a dimer problem, firs t considered by physicists, at the intersection of graph theory and enumera tive combinatorics. I’ll review some highlights in the theory of dimers, di splaying elegant formulas for the number of tilings and striking pictures o f the kinds of long-range order that can arise spontaneously.
Then I’ ll discuss beautiful work of Conway, Lagarias, and Thurston applying combin atorial group theory to the study of tiling problems, yielding criteria for distinguishing between doable and non-doable tiling problems. I’ll apply t he method to obtain a surprising result about a class of tiling problems th at are ALMOST never doable.
Finally, bringing the two strands together , I’ll discuss my recent empirical work counting tilings related to trimer models. None of the methods that I know of for obtaining exact formulas for dimers apply here, yet the data show a wealth of patterns suggesting that there are deep theorems to be proved. Especially mysterious are some patter ns involving the 2-adic numbers.
This talk should be understandable to undergraduates. No background in graph theory, enumerative combinatorics, combinatorial group theory, or p-adic analysis will be required, and you wo n’t need to know what a dimer or a trimer is when you arrive (though you wi ll when you leave).

CONTACT:James Propp (UMass, Lowell) DTSTAMP:20260827T005740 DTSTART;TZID=America/New_York:20220330T153000 DTEND;TZID=America/New_York:20220330T163000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR