The Arithmetic of Power Series
A 2022 AustMS Mahler Lecture presented by Frank Calegari
Speakers
Content navigation
RegisterDescription
The Mahler lectures are a biennial activity organised by the Australian Mathematical Society, and supported by the Australian Mathematical Sciences Institute. The tour invites a prominent international mathematician to travel to Australian universities to deliver lectures at a variety of levels, including several public lectures.
Abstract
A holomorphic function $P(z)$ of a complex variable around $z = 0$ has a power series expansion $P(z) = \sum a_n z^n$. What constraints are imposed on $P(z)$ by assuming that all the coefficients $a_n$ are integers? We discuss some variations on this problem starting with some very elementary observations and leading up to a resolution of a 50 year old conjecture, as well as the surprising links to differential equations and group theory.
About the author
Born in Melbourne, Frank Calegari attended Melbourne University as an undergraduate and completed his graduate studies at the University of California at Berkeley and a postdoctoral fellowship at Harvard University. He joined the Faculty of Northwestern University in 2006 and has since been a Fellow of the American Mathematical Institute and a von Neumann Fellow of Mathematics at the Institute for Advanced Study. Frank has been a Professor of Mathematics at the University of Chicago since 2015. His numerous awards include a Sloan Fellowship (2009) and in 2013 he become a fellow of the American Mathematical Society.
His research is in the area of algebraic number theory. Frank is particularly interested in the Langlands programme, especially, the notion of reciprocity linking Galois representations and motives to automorphic forms. For reprints and preprints, please visit the research page on his website. Frank is a former American Institute of Mathematics 5-year fellow.
Frank’s other interests include coffee, cooking, cricket, and classical piano, and he has even performed live with Zubin Mehta and the Israeli Philharmonic Orchestra.
Zoom Details:
Topic: The Arithmetic of Power Series
Time: Nov 28, 2022 04:00 PM Canberra, Melbourne, Sydney
Join Zoom Meeting
https://anu.zoom.us/j/84744597590?pwd=NVN2WnIrZGwvMEZKNFVvOG1nTlplUT09
Meeting ID: 847 4459 7590
Password: 942860
One tap mobile
+61280156011,,84744597590#,,,,0#,,942860# Australia
+61370182005,,84744597590#,,,,0#,,942860# Australia
Dial by your location
+61 2 8015 6011 Australia
+61 3 7018 2005 Australia
+61 7 3185 3730 Australia
+61 8 6119 3900 Australia
+61 8 7150 1149 Australia
Meeting ID: 847 4459 7590
Password: 942860
Find your local number: https://anu.zoom.us/u/kbtncIuN7y
Or an H.323/SIP room system:
Dial: +61262227588 (AUCX)
or 84744597590@zoom.aarnet.edu.au
Meeting ID: 84744597590
H323/SIP Password: 942860
Join by Skype for Business
https://anu.zoom.us/skype/84744597590
Location
Seminar Room 1.33
Hanna Neumann Building 145
Science Road
Acton ACT 2601