Activities This Week

This is part 1 of the speaker’s talk from last semester, expanded into a two-part series.

The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:G^->H^ between their dual complex groups should naturally give rise to a map r*:Rep(G)->Rep(H) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.

We will consider a class of groups defined by their action on Cantor space and use the invariant of finiteness properties to find among these groups an infinite family of quasi-isometry classes of finitely presented simple groups.

This is a joint work with Stefan Witzel and Matthew C. B. Zaremsky.

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups G such that every element of G is contained in a compact open normal subgroup of G. For continuous endomorphisms ϕ:G→G of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.

This is joint work with Anna Giordano Bruno and Daniele Toller.

בקונגרס הבינלאומי במתמטיקה שהתקיים בשנת 1900 הציג דוד הילברט 23 בעיות פתוחות בכל התחומים של מתמטיקה. חלקן נפתרו (או נפתרו חלקית) וחלקן פתוחות עד היום.

הבעיה השלישית ברשימה התייחסה לקיום של פאונים בעלי נפחים זהים אך כאלה שלא ניתן לפרקם למספר סופי של תת פאונים חופפים. בעיה זו נפתרה תוך שנתיים ע”י תלמידו של הילברט – מקס דן. בהרצאה נדבר על הבעיה המקורית, על פתרונה ועל בעיות קשורות.