Integrated Calendar

For a Nash manifold X and a Nash vector bundle E on X, one can form the topological vector space of Schwartz sections of E, i.e. the smooth sections which decay fast along with all derivatives. It was shown by Aizenbud and Gourevitch, and independently by Luca Prelli, that for a Nash manifold X, th complex of Schwartz sections of the de Rham complex of X has cohomologies isomorphic to the compactly supported cohomologies of X.

In my talk I will present a work in progress, joint with Avraham Aizenbud, to generalize this result to the relative case, replacing the Nash manifold M with a Nash submersion f:M--

Consider the function field $F$ of a smooth curve over $FF_q$, with $q
eq 2$.

L-functions of automorphic representations of $GL(2)$ over $F$ are important objects for studying the arithmetic properties of the field $F$. Unfortunately, they can be defined in two different ways: one by Godement-Jacquet, and one by Jacquet-Langlands. Classically, one shows that the resulting L-functions coincide using a complicated computation.

I will present a conceptual proof that the two families coincide, by categorifying the question. This correspondence will necessitate comparing two very different sets of data, which will have significant implications for the representation theory of $GL(2)$. In particular, we will obtain an exotic symmetric monoidal structure on the category of representations of $GL(2)$

It turns out that an appropriate space of automorphic functions is a commutative algebra with respect to this symmetric monoidal structure. I will outline this construction, and show how it can be used to construct a category of automorphic representations.

Zoom meeting:

The current research draws a timeline of development and change in the Levantine silver trade and its impact on humans from the end of Bronze Age to Iron Age II (~1200 to ~700 BCE). Silver, extracted from Pb-rich minerals was used as the main currency in the Levant during this period, and was transported to the Levant from Anatolia, the Aegean islands, Sardinia, and Iberia through maritime routes.
For achieving the research goal, we combined detailed archaeological, chemical and isotopic analyses of more than 160 silver objects and 60 human teeth. During the Late Bronze Age and Iron Age I, silver was transported from Anatolia and the Aegean islands. Following the collapse of the Late Bronze Age trade network, a major shortage in silver in the Levant occurred, leading to extensive forgery. Initially, it involved addition of copper from Timna probably by the Egyptians, and later from Faynan. Arsenic was added as well to conceal the addition of copper. Only during the 10th century BCE did a new source of silver in the Levant appear: Silver mined from Pb-deposits in Anatolia and southwest Sardinia, brought by the Phoenicians. This marked the end of silver forgery in the Levant. A century later, the Phoenicians conveyed silver from Iberia, a source that supplied large quantities of silver throughout the 9th and 8th centuries BCE.
Analysis of human teeth showed that people living in the Levant during this period were affected by metal use and trade. Approximately 15% of the population was polluted, and the majority of the polluted individuals were associated with coastal or marine habitats. We also show that during Iron Age I and II, the coastal population in the Levant had different chemical and isotopic characteristics than the inland population.

The lecture is in Hebrew