Category Archives: Announcements

An assistant professor position in mathematical logic, Charles University in Prague, Deadline: 31 October 2014

The Department of Algebra invites applications for a tenure-track position at the rank of assistant professor in the area of mathematical logic. The expected starting date is January 1, 2015 or soon afterwards and is negotiable.

Areas of special interest are:
(i) interactions of logic with computational complexity theory, or
(ii) model theory (any of its facets).
However, strong candidates in all areas of mathematical logic will be considered. Candidates are required to have a proven international research record corresponding to their career stage and a postdoctoral experience.

A successful candidate is expected to pursue an active research program, teach advanced and introductory classes in Czech and/or English and possibly supervise undergraduate and graduate students. Teaching in Czech is not required. (English is sufficient since the advanced classes may be taught in English even in standard undergraduate programs.)

The expected duration of the initial contract is three years. Such a position is renewable under a mutual agreement for another three years (and possibly for further three years, depending on the career stage). These new contracts depend on how successfully the assistant professor carries out research and teaching duties. Then, subject to a separate review process (called a habilitation), a promotion to the rank of associate professor is usual. This promotion is usually connected with a tenure. However, if the candidate’s career is already advanced with a strong research record, the initial period can be substantially reduced and you can progress to the promotion very fast.

Electronic applications accompanied by:

a curriculum vitae
a proof of PhD in a relevant field
a list of publications
a description of pedagogical experience

should be sent to Mrs. Eva Ramesova at ramesova@karlin.mff.cuni.cz.
The candidate should also arrange for two letters of recommendation to be sent directly to the same address. Informal inquiries are welcome and may be sent to Prof. Jan Krajicek at krajicek@karlin.mff.cuni.cz.
The application deadline is October 31, 2014.

Early applications are encouraged; applications may be processed as they are received.

We may invite the best candidates for an interview during October – mid November; after that the final round of selection will follow.

http://www.karlin.mff.cuni.cz/katedry/ka/ka.htm
http://www.mff.cuni.cz/to.en/fakulta/prace/

Postdoctoral position in mathematical logic (3y), Freiburg (Germany), Deadline: 25 July 2014

Postdoctoral position in mathematical logic (3y), Freiburg (Germany), Deadline: 25 July 2014

The Section for Mathematical Logic of the Universitaet Freiburg invites
applications for an Assistant’s position at level A13 or E13. Fulltime
position, start date: 01.10.2014
The teaching load is four hours per week during the term in a field of mathematical logic or in the beginners’ education in mathematics.
Prerequisites are a Ph.D. and possibly further research in set theory. Moreover, there is the possibility to obtain the habilitation degree. There is the possibility to prolong the contract by another three years.
Employment as a civil servant is subject to certain conditions, among them a Ph.D. with grade at least magna cum laude (if graded at all). The position can be filled by October 1, 2014 or later.

Applicants please send a cv, certificates, transcripts, a publication list
and a research proposal and the filled-in application form
(http://www.zuv.uni-freiburg.de/formulare/bewerbungsbogen_englisch.pdf)
per e-mail to Prof. Dr. Heike Mildenberger. The address is
heike.mildenberger@math.uni-freiburg.de
See further informations at http://logik.mathematik.uni-freiburg.de

The contract is a fixed-term contract for 3 years . The salary will be determined in accordance with A13 or E13. The university is currently seeking to increase the amount of female employees and is thus especially pleased to receive applications from qualified females.

Please send applications including a printout of the application form and
the usual documentation to the following address by 25.07.2014.
Applications should be marked with the reference number 8839
heike.mildenberger@math.uni-freiburg.de For further information, please
contact Heike Mildenberger at Tel. +49 761 2035603 or E-mail
heike.mildenberger@math.uni-freiburg.de.

http://www.uni-freiburg.de/administration/stellenboerse?erf=y&stellenid=8839&layout=v4&set_language=en

reminder: Ramsey Theory Conference: May 24-28

Ramsey theory conference
University of Denver. May 24–28, 2014

https://portfolio.du.edu/ramsey

The aim of this conference is to bring together students and researchers from around the world in the field of Ramsey Theory. The focus is on structural and infinitary Ramsey theory and applications to other fields of mathematics, including Banach spaces, Boolean algebras, Set Theory, and Topological Dynamics. The conference will consist of a large number of plenary talks and contributed talks of 25 minutes. The official language of the conference is English. As part of the DU Sesquicentennial Celebration, this conference celebrates the contributions of George Boole (1815-1864) to Ramsey Theory and Boolean Algebras.

Invited speakers (confirmed so far):

· Antonio Aviles (University of Murcia, Spain)
· Dana Bartosova (University of Sao Paulo, Brazil)
· Andreas Blass (University of Michigan, USA)
· Ari Brodsky (University of Toronto, Canada)
· Carlos Di Prisco (Instituto Venezolano de Investigaciones Científicas, Venezuela)
· Neil Hindman (Howard University, USA)
· Michael Hrusack (Universidad Nacional Autónoma de México, Mexico)
. Alexander Kechris (Cal Tech, USA)
· Jean Larson (University of Florida at Gainsville, USA)
· Brice Mbombo (University of Sao Paulo, Brazil)
· Diana Ojeda (Cornell University, USA)
· Claribeth Pina, (University of Paris 7, France)
· Slawomir Solecki (University of Illinois at Urbana-Champaign, USA)
· Dona Strauss (University of Leeds, UK)
· Stevo Todorcevic (University of Toronto, Canada/ University of Paris 7, France)
· Timothy Trujillo, (University of Denver, USA)
· Anush Tserunyan (University of Illinois at Urbana-Campaign, USA)

Scientific committee:

· Natasha Dobrinen (University of Denver)
· José G. Mijares (University of Denver)

Organizing committee:

· Alvaro Arias (University of Denver)
· Natasha Dobrinen (University of Denver), Chair
· José G. Mijares (University of Denver)
· Timothy Trujillo (University of Denver)

Two years fellowship at the University of Torino

The University of Torino (together with the Compagnia di San Paolo and the European union) is offering 14 Train2Move fellowships in several areas, including mathematics.

Among the many eligible proposed fellowships there is one entitled Descriptive set theory. Now there is the call for applications, and we kindly are asking you to inform any person that may be interested.
The fellowship gives:
a gross salary of 37,500 euro per year, for two year (roughly 1,900 euro per month net)
a travel grant 8,500 euro per year
Eligibility. The candidates should
have not spent more than one year in Italy (for work) during the last three years,
have received a PhD no more than seven year form May 2014
For more on this fellowship, including how to apply,  see
Contact Alessandro Andretta or  Matteo Viale for details.

Postdoc Position in Set Theory in Torino (Italy), 2014-2015

16 MONTHS POSTDOC POSITION IN SET THEORY IN TORINO (ITALY)

There is an opening for a 16 months post doc position in set theory in the department of mathematics of Torino university starting may 1st 2014 and finishing august 31st 2015. Applicants are required to be less than 35 and must have earned their Ph.D. title. It is also required to the applicants to have at least one publication in a peer reviewed journal in the last three years. The net salary is slightly more than 1400 euros per month which allow for a reasonable living in Torino, extra money for research and travel can be given. The post doc will join the logic group of the department which consists of Matteo Viale, Alessandro Andretta, Riccardo Camerlo (polytechnical university), Daisuke Ikegami (set theory), Domenico Zambella (model theory). In the fall Daisuke Ikegami will leave and Luca Motto Ros (currently in freiburg) will most likely join the group. The selection of applicants will be based on an evaluation of the CV, of the publication records, and of their interests of research which must be in set theory. It is possible to file online the applications creating an account on the italian ministry of education website. If you intend to apply write to matteo.viale@unito.it in order to get detailed information on the filing procedure.
Applicants can deposit their online registration forms since today up to the 19th of march 2014.
Those passing a first selection will be admitted to a (skype) interview which will take place most likely in the end of march-beginning of April. The position starts at the earliest on may 1st 2014, but the starting (not the ending period) can eventually be delayed.
Due to a very restrictive law on immigration, non EU-applicant should consider that the constraint on the expiration of the grant and the time required to get their working visa may shorten significantly the length of the period in which they can use the grant.

15-819 Homotopy Type Theory

Folks,
Some of you may be interested in this course, running this semester.
It starts next week.

 

15-819 Homotopy Type Theory

Synopsis

This is a graduate research seminar on Homotopy Type Theory (HoTT), a recent enrichment of Intuitionistic Type Theory (ITT) to include “higher-dimensional” types. The dimensionality of a type refers to the structure of its paths, the constructive witnesses to the equality of pairs of elements of a type, which themselves form a type. In general a type is infinite dimensional in that it exhibits non-trivial structure in that it has elements, paths between elements, paths between paths between elements, and so on to all finite levels. Moreover, the paths at each level exhibit the algebraic structure of a (higher) groupoid, meaning that there is always the “null path” witnessing reflexivity, the “inverse” path witnessing symmetry, and the “concatenation” of paths witnessing transitivity such that group-like laws hold “up to higher homotopy”. This means that there are higher-dimensional paths witnessing the associative, unital, and inverse laws for these operations. Altogether this means that, in brief, a type is a weak ∞-groupoid.

The significance of the higher-dimensional structure of types lies in the concept of a type-indexed family of types. Such families exhibit the structure of a fibration, which means that a path between two indices “lifts” to a transport mapping between the corresponding instances of the family that is, in fact, an equivalence. Thinking of paths as constructive witnesses for equality, this amounts to saying that equal indices give rise to equivalent types, and hence, by univalence, equal elements of the universe in which the family is valued. Thus, for example, if we think of the interval I as a type with two endpoints connected by a path, then an I-indexed family of types must assign equivalent types to the endpoints. In contrast the type B of booleans consists of two disconnected points, so that a B-indexed family of types may assign unrelated types to the two points of B. Similarly, mappings from I into another type A must assign connected points in A to the endpoints of the interval, whereas mappings from B into A are free to assign arbitrary points of A to the two booleans. These preservation principles are central to the structure of HoTT. Indeed, one may say that the entire subject amounts to a careful analysis and extension of the concept of equality in intuitionistic type theory.

In many cases the path structure of a type becomes trivial beyond a certain dimension, called the level of the type. By convention the levels start at -2 and continue through -1, 0, 1, 2, and so on indefinitely. At the lowest, -2, level, the path structure of a type is degenerate in that there is an element to which all other elements are equal; such a type is said to be contractible, and is essentially a singleton. At the next lowest level, -1, the type of paths between any two elements is contractible (level -2), which means that any two elements are equal, if there are any elements at all; such as type is a sub-singleton or h-proposition. At the next level, 0, the type of paths between paths between elements is contractible, so that any two elements are equal “in at most one way”; such a type is a set whose types of paths are all h-prop’s. Continuing, types of level 1 are groupoids, those of level 2 are 2-groupoids, and so on for all finite levels.

ITT is capable of expressing only sets, types of dimension 0. Such types may have elements, and two elements may be considered equal in at most one way. A large swath of (constructive) mathematics may be formulated using only sets, and hence is amenable to representation in ITT. Computing applications, among others, require more than just sets. For example, it is often necessary to suppress distinctions among elements of a type so as to avoid over-specification; this is called proof irrelevance. Traditionally ITT has been enriched with an ad hoc treatment of proof irrelevance by introducing a universe of “propositions” with no computational content. In HoTT such propositions are types of level -1, requiring no special treatment or distinction. Such types arise by propositional truncation of a type to render degenerate the path structure of a type above level -1, ensuring that any two elements are equal in the sense of having a path between them.

Propositional truncation is just one example of a higher inductive type, one that is defined by specifying generators not only for its elements, but also for its higher-dimensional paths. The propositional truncation of a type is one that includes all of the elements of the type, and, in addition, a path between any two elements, rendering them equal. It is a limiting case of a quotient type in which only certain paths between elements are introduced, according to whether they are deemed to be related. Higher inductive types also permit the representation of higher-dimensional objects, such as the spheres of arbitrary dimension, as types, simply by specifying their “connectivity” properties. For example, the topological circle consists of a base point and a path starting and ending at that point, and the topological disk may be thought of as two half circles that are connected by a higher path that “fills in” the interior of the circle. Because of their higher path structure, such types are not sets, and neither are constructions such as the product of two circles.

The univalence axiom implies that an equivalence between types (an “isomorphism up to isomorphism”) determines a path in a universe containing such types. Since two types can be equivalent in many ways (for example, there can be distinct bijections between two sets), univalence gives rise to types that are not sets, but rather are of a higher level, or dimension. The univalence axiom is mathematically efficient because it allows us to treat equivalent types as equal, and hence interchangeable in all contexts. In informal settings such identifications are often made by convention; in formal homotopy type theory such identifications are true equations.

 

BEST 2013 slides and photos

Photos

Album

Talks

Lynne Yengulalp – From subcompact to domain representable
Kostas Beros – Universal subgroups
Shehzad Ahmed – Admissible determinacy
Marion Scheepers – Remarks on countable tightness
Todd Eisworth – Higher cardinal characteristics and PCF
Kameryn Williams – A generalization of the notion of strong measure zero to quasi uniform spaces
David Chodounsky – Hausdorff gaps and towers
Masaru Kada – How many miles to beta(omega), after all?
Jay Williams – Cone measures and bi-embeddability of Kazhdan groups
Timothy Trujillo – A Ramsey classification theorem with an application to the Tukey theory of ultrafilters
Scott Schneider – Locally nilpotent group actions and hyperfinite equivalence relations
Thilo Weinert – Partition relations for linear orders in a non-choice context
Grigor Sargsyan – Some new applications of core model induction

Postdoc position in Set Theory in Torino (July 2013 to June 2015)

There is an opening for a two year post-doc position in set theory in the department of mathematics of Torino university starting july 1st 2013 and finishing june the 30th 2015.

Applicants are required to be less than 35 and must have earned their Ph.D. title. It is also required to the applicants to have at least one publication in a peer reviewed journal in the last five years. The net salary is slightly more than 1400 euros per month. The post doc will join the logic group of the department which consists of Matteo Viale, Alessandro Andretta, Raphael Carroy (set theory), Domenico Zambella (model theory).

The selection of applicants will be based on an evaluation of the CV, of the publication records, and of their interests of research which must be in set theory. It is possible to file online the applications creating an account on the italian ministry of education website. If you intend to apply write to matteo.viale@unito.it in order to get detailed information on the filing procedure.

Applicants can deposit their online registration forms since the 7th of may 2013 up to the 28 of may 2013. Those passing a first selection will be admitted to a (skype) interview which will take place between the 5th and the 7th of june 2013.

no seminar this week

Rutgers Logic Seminars
Spring 2013
Rooms 423 & 705, Hill Center

Descriptive Set Theory Seminar
Hill 423
Monday April 29th, 3:20-4:40 pm
No seminar this week

Rutgers Logic Seminar
Hill 705
Monday April 29th, 5:00-6:20 pm
No seminar this week

Simplicity meeting: Woodin and Sargsyan

Speaker: Hugh Woodin
Time: Thursday April 4rth at 3:45.
Location: CUNY Graduate Center, Proshansky Auditorium

Panelist: Grigor Sargsyan
Times: 1:30-02:30 Thursday April 4 and 5th
Location: CUNY Graduate Center, Proshansky Auditorium

See here.