## Summer School in Explicit Methods for Abelian Varieties

- Start Date: 06/16/2016
- End Date: 06/18/2016

Confirmed speakers and topics:

- Jennifer Balakrishnan (University of Oxford): p-adic heights on Jacobians of hyperelliptic curves

- Lassina Dembélé (University of Warwick): abelian surfaces with everywhere good reduction

- Jan Steffen Müller (University of Oldenburg): canonical heights on Jacobians of hyperelliptic curves

- Rachel Pries (Colorado State University): open questions for Jacobians of curves over finite fields

University of Calgary

**Location**: University of Calgary, Mathematical Sciences Building

**Registration**: There is no registration fee, but space is limited and will be granted on a competitive basis with priority given to graduate students. Partial funding will also be awarded to a limited number of student participants. Applicants should proceed as follows:

- Sign up by clicking on the "SIGN UP" button at the bottom of the page and proceed as instructed

- E-mail the following information to pimsadm@ucalgary.ca by April 15, 2016:

* Full name, e-mail address, institution, status (postdoc, student); for students: degree program and year

* Brief statement describing why they wish to participate in the summer school*For student applicants: name and e-mail address of supervisor

- Student applicants should also arrange for their supervisor to e-mail a brief letter of support to pimsadm@ucalgary.ca.

Successful applicants will be notified by April 22, 2016. For questions and inquiries, please contact Mike Jacobson at jacobs@ucalgary.ca

**June 16:**

8:50- 9:00 Opening remarks

9:00- 9:50 Rachel Pries (Lecture 1)

10:00-10:50 Steffen Mueller (Lecture 1)

10:50-11:15 Coffee break

11:15-12:05 Jennifer Balakrishan (Lecture 1)

12:05-14:00 Lunch break

14:00-14:50 Lassina Dembele (Lecture 1)

15:00-16:00 Problems

16:00-16:30 Coffee break

16:30 -18:00 Problem session

**June 17:**

9:00- 9:50 Rachel Pries (Lecture 2)

10:00-10:50 Steffen Mueller (Lecture 2)

10:50-11:15 Coffee break

11:15-12:05 Jennifer Balakrishnan (Lecture 2)

12:05-14:00 Lunch break

14:00-14:50 Lassina Dembele (Lecture 2)

15:00-16:00 Problem session

16:00-16:30 Coffee break

16:30 -18:00 Problem session

**June 18:**

9:00-12:00 To be determined

**Summer School Materials:**

Rachel Pries’ Materials:

Jennifer Balakrishnan’s Materials:

Steffen Mueller’s Materials:

Lassina Dembele’s Materials:

**Venue:**

All lectures will take place in ST 139 in the Science Theatre Complex on the University of Calgary campus. Coffee breaks will take place in MS 461, the lounge on the 4th floor of the Mathematical Sciences Building. Consult the U of C Interactive Room Finder at http://ucmapspro.ucalgary.ca/RoomFinder/ or the campus map (in PDF) at http://ucmaps.ucalgary.ca/PublicFiles/CurrentMaps/CampusMap_MainCampus_L....

**Food:**

Participants are asked to secure their own meals. A variety of fast food options are available in the Student Union (MacEwan Student Centre) and at other locations across campus. There are also three pubs in MacEwan that are open during the day. Coffee shops can be found all across campus, including Good Earth Coffeehouse in the Taylor Family Digital Library and the ICT Building, Starbucks in the basement of MacEwanHall, and other coffee shops on the man floor of MacEwan Hall and the Science Theatre area near the Social Sciences complex.

**Preparation:**

Basic familiarity with elliptic curves (at the level of Silverman's "Arithmetic of Elliptic Curves") is assumed for most of the lectures.

For Dr Balakrishnan's and Dr Mueller's lectures:

- familiarity with basics of hyperelliptic curves and their Jacobians s expected, as in sections 2 and 4 of Stoll's notes on the arithmetic of hyperelliptic curves, available at http://www.mathe2.uni-bayreuth.de/stoll/teaching/ArithHypKurven-SS2014/S....
- familiarity with basics of arithmetic surfaces and their intersection theory, as in, for instance, sections IV.4 and IV.7 of Silverman's "Advanced Topics in the Arithmetic of Elliptic Curves", is helpful.

For Dr Dembele's lectures, he recommends the following background reading:

- Sections 1-4 of his notes with John Voight: http://arxiv.org/pdf/1010.5727.pdf
- Noam Elkies' notes on elliptic curves with everywhere good reduction: http://math.harvard.edu/~elkies/rqfu/. There are useful references in there about such elliptic curves.
- His joint paper with A. Kumar: http://arxiv.org/pdf/1309.3821.pdf

Computational resources used for some of the lectures and problems van be found at the following websites:

- SAGE: https://cloud.sagemath.com
- MAGMA online calculator: http://magma.maths.usyd.edu.au/calc/

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Full scientific report available here.