Department of Mathematics Calendar

Back to Listing

The Department of Mathematics Calendar has moved to Webtools. Anyone may submit an event by clicking the "+" button (upper right). Note: the Sponsor field is required. Just type "n/a"

All events will be reviewed before acceptance. Please email Shelby Koehne if you have any questions about submitting an event.

Note: you may search past and future events by clicking on the magnifying glass icon on the main Calendar page.

For an archive of past events: https://math.illinois.edu/research/seminars-department-calendar

Graph Theory and Combinatorics Seminar: Rational exponents for generalized extremal problems

Event Type
Seminar/Symposium
Sponsor
N/A
Location
345 AH
Date
May 3, 2022   1:00 pm  
Speaker
Anastasia Halfpap (University of Montana)
Contact
Sean English
Views
15
Fix a target graph H and a family F of forbidden graphs. The generalized extremal number ex(n, H, F) is the maximum number of H-copies possible in an n-vertex graph which avoids F. Note that when H is an edge, ex(n, H, F) is the ordinary extremal number ex(n, F). After the systematic study of generalized extremal numbers was initiated by Alon and Shikhelman in 2016, the area has received substantial attention. In addition to explicit computation of ex(n, H, F) for specific choices of H, F, many questions in extremal graph theory (e.g., supersaturation, stability) naturally extend to the generalized setting.
 
In 2015, Bukh and Conlon applied the random algebraic method to show that, for any rational r in the interval [1,2], there is a family such that ex(n, F) = Theta(n^r).  Analogously, for a fixed target graph H and a rational number r within an appropriate interval, we may ask whether it is possible to find a forbidden family for which ex(n, H, F) = Theta(n^r). In this talk, we present results on this question for some specific target graphs H, focusing on the case where H is a triangle, for which we show that all rational exponents in [1,3] are realizable. Joint work with Sean English and Bob Krueger. 
link for robots only