Abstract: It has long been known that two independent copies of the infinite Erdos-Renyi graph G(\infty,p) are almost surely isomorphic. The resulting graph is called the Rado graph. If the vertices are in a metric space and only nearby vertices may be connected, a similar result may or may not hold, depending on fine details of the underlying metric space. We present new results in the case where the metric space is a circle.
Using the axiom of choice one can construct set of reals which are
pathological in some sense. Similar constructions can be produce such
"pathological" subsets of any non trivial Polish space (= a complete
separable metric space).
A "pathological set" can be a non measurable set , a set which does
not have the property of Baire (namely it is not a Borel set modulo a
rst category set).
A subset of the innite subsets of natural numbers,
can be considered to be "pathological" if it is a counter example to
Using the axiom of choice one can construct set of reals which are
pathological in some sense. Similar constructions can be produce such
"pathological" subsets of any non trivial Polish space (= a complete
separable metric space).
A "pathological set" can be a non measurable set , a set which does
not have the property of Baire (namely it is not a Borel set modulo a
rst category set).
A subset of the innite subsets of natural numbers,
can be considered to be "pathological" if it is a counter example to
Eliana Bariga will speak about Definably compact semialgebraic groups over real closed fields.
Abstract: Semialgebraic groups over a real closed field can be seen as a generalization of the semialgebraic groups over the real field, and also as a particular case of the groups definable in an o-minimal structure.
January 16, 12:00-13:00, Seminar room 209, Manchester building.
Abstract: I plan to show a proof of the statement "residually-finite-by-residually-finite extensions are weakly sofic". The proof is based on characterization of weakly sofic groups by solvability of equations over groups. It looks different from other proofs of soficity and weak soficity. I plan to discuss relations of equations on and over groups with soficity in some details.
OAntongiulio Fornasiero will speak about definable and interpretable groups and fields in the p-adics.
Abstract: A. Pillay showed that every definable group in the p-adics has a canonical topology and differential structure, and deduced that every definable field is either finite or a finite extension of Q_p. In a joint work with J. de la Nuez Gonzalez we extend the analysis to interpretable fields, and show that they are either countable or finite extensions of Q_p.
ד"ר יובל נוב: צלילים, מספרים, מנגינות וכיוונים - מפיתגורס עד ימינו
צלילים ומנגינות הם תופעות המקיימות חוקיות מתמטית. ההרצאה תציג את החוקיות הזו, ובעיקר תעסוק ב"בעיית הכיוון" של כלי נגינה, ובפתרונות המתמטיים שהוצעו לה במהלך הדורות. ההרצאה מלווה בדוגמאות רבות, ואינה דורשת ידע מוקדם במוזיקה.
פרופ' עמנואל פרג'ון: הגאומטריה של הזמן - לפי איינשטיין וחבריו
לפני כ-100 שנה נצפתה סטיה קלה של אורות כוכבים ממסלולם בעוברם ליד השמש. הסטיה התאימה בקירוב לגישתו הגאומטרית של איינשטיין להבנת הזמן וכח הכבידה, הגרוויטציה הניוטונית. ענף רחב ידים של המתמטיקה, הגאומטריה של רימן, גאוס, לוי-צ'יביטה ורבים אחרים קיבל תנופה רבה כבסיס מתמטי לגאומטריה של המרחב-זמן שפותחה ע"י איינשטיין.
