Intercity Number Theory Seminar

Hendrik Lenstra's sixtieth birthday

April 24, Leiden.

A special day at the occasion of Hendrik Lenstra's sixtieth birthday will be held on April 24 in Leiden. The morning program contains two mathematical talks and is part of the workshop Counting Points on Varieties. The afternoon will feature more personal talks by friends and colleagues of Hendrik Lenstra. Everybody is welcome to attend.

Morning program in the De Sitterzaal, Oort building:

  •  9:15: coffee
  •  9:45: opening
  •  9:50 - 10:40: Carl Pomerance (Dartmouth)
  • 10:50 -11:40: Manjul Bhargava (Princeton)

Afternoon program in the Lorentzzaal (A144) Kamerlingh Onnes Gebouw, Steenschuur 25, Leiden.

  • 14:00 - 14:25: Ed Schaefer (Santa Clara)
  • 14:30 - 14:55: Everett Howe (San Diego)
  • 15:00: coffee
  • 15:30 - 15:55: Johannes Buchmann (Darmstadt)
  • 16:00 - 16:25: Richard Groenewegen (London)
  • 16:30: closing and drinks

Organisers: Ronald van Luijk, Bart de Smit, Peter Stevenhagen, Lenny Taelman.

09:50–10:40
Carl Pomerance, Sociable numbers
Consider iterating the function which sends a natural number to the sum of its proper divisors. A fixed point for this system, such as 6 or 28, is called perfect, while a number belonging to a cycle of length 2, such as 220 or 284, is called amicable. Known to Euclid and Pythagoras, some scholars have even found allusions to perfect and amicable numbers in the Old Testament. Sociable numbers are the natural generalization of perfect and amicable numbers to cycles of arbitrary length - they are mere youngsters, having been studied for only a century! This talk will describe the colorful history of the problem (with more connections to Hendrik Lenstra than you might imagine) and report on some recent results on the distribution of sociable numbers within the natural numbers.
10:50–11:40
Manjul Bhargava, Galois closure for rings
Abstract: We all learn the notion of "Galois closure" or "normal closure" for a finite extension of fields. But what might we mean by the "Galois closure" of an extension of rings? (joint work with Matthew Satriano; based on conversations with Hendrik Lenstra, Jean-Pierre Serre, Bart de Smit, and Kiran Kedlaya)
14:00–14:25
Ed Schaefer, I started feeling sorry for the problem.
14:30–14:55
Everett Howe, Channeling your advisor
15:30–15:55
Johannes Buchmann, Hendrik Lenstra and cryptography
16:00–16:25
Richard Groenewegen, A sense of reality