# Prof. Dr. Jens Franke

## Sprechstunden

Freitags, von 14.20 bis 15.20, in meinem Büro (1.026).

## Lecture "Algebraic geometry II"

The exercises are on Thursdays 16.15 in N0.007.

## Lecture "Selected Topics in Algebra" (Homological methods in commutative algebra).

The lecture takes place on Fridays 8.15 to 9.45 in Gr. Hs.
## Vorlesung "Algebra II"

- Corrected version of first exercise sheet, due October 23.
- Second exercise sheet, due October 30.
- Third exercise sheet, due November 6.
- Corrected version of fourth exercise sheet, due November 13.
- Fifth exercise sheet, due November 20.
- Sixth exercise sheet, due November 27.
- Seventh exercise sheet, due December 4.
- Eighth exercise sheet, due December 11.
- Ninth exercise sheet, due December 18.
- Tenth exercise sheet, due January 8.
- Eleventh exercise sheet, due January 15.
- Twelfth exercise sheet, due January 22.

## Lecture "Algebraic Geometry I"

- Corrected version of first exercise sheet, due October 24.
- Second exercise sheet, due November 3.
- Third exercise sheet, due November 10.
- Fourth exercise sheet, due November 17.
- Corrected version of fifth exercise sheet, due
November 24.
- Corrected version of sixth exercise sheet, due December 1.
- Seventh exercise sheet, due December 8.
- Eighth exercise sheet, due December 15.
- Nineth exercise sheet, due December 22.
- Tenth exercise sheet, due January 12.
- Eleventh exercise sheet, due January 19.
- Eleventh exercise sheet, due January 26.

## Seminar "Geometrische Konstruktionen und transzendente Zahlen."

Das Seminar fand im Sommersemester 2016 für Studenten des zweiten Semesters
statt. Um einen guten Anschluß an die Vorlesung
"Lineare Algebra I" sicherzustellen, diente

ein von mir
selbst verfaßter Text als Grundlage des Seminares. Dieser soll hier
weiterhin zur Verfüfung gestellt werden.

## Vorlesungen "Mathematik für Physiker I-III"

Die Javascript-Programme zu den Anwesenheitsübungen dieser Vorlesungen, die
ich zwischen 2008 und 2011 gehalten habe, sind weiterhin online:

## Selected Publications

**On the spaces F**^{s}_{pq} of Triebel-Lizorkin type:
pointwise multipliers and spaces on domains, Math. Nachr. 125 (1986),
113-149.
- (with Yu. I. Manin and Yu. Tschinkel)
**Rational points of bounded height on Fano varieties,**
Invent. Math. 95(1989), 421-435
- (with T. Runst)
**Regular elliptic boundary value problems in Besov-Triebel-Lizorkin spaces.
**
Math. Nachr. 174 (1995), 113-149.
**Harmonic analysis in weighted L**_{2}-spaces,
Ann. Sci. École Norm. Sup. (4), 31(1998), 181-279
- (with J. Schwermer),
**A decomposition of spaces of automorphic forms, and the Eisenstein
cohomology of arithmetic groups,**
Math. Ann. 311(1998), 765-790.
**On the singularities of residual Eisenstein series,**
Invent. Math. 138(1999), 307-317
- (With T. Kleinjung, F. Morain and T. Wirth)
**Proving the primality of very large numbers with fastECPP,**
in **Algorithmic number theory,**
Lecture Notes in Comput. Sci., 3076, 2004, pages 194-207.
- (With T. Kleinjung),
Continued fractions and lattice sieving.
In: Proceedings SHARCS 2005
- (with K. Aoki, T. Kleinjung, A. Lenstra, D. Osvik)
**A kilobit special number field sieve factorization,**
in **Advances in cryptology. ASIACRYPT 2007,**
Lecture Notes in Comput. Sci., 4833, 2007, pages 1-12.
** A topological model for some summand of the Eisenstein
cohomology of congruence subgroups**, in
**Eisenstein series and applications,** Progr. Math., 258, 2008,
pages 27-85.