Tue, 29 May 2018

12:00 - 13:00
C3

Towards an Integrated Understanding of Neural Networks

David Rolnick
(MIT)
Abstract


Neural networks underpin both biological intelligence and modern AI systems, yet there is relatively little theory for how the observed behavior of these networks arises. Even the connectivity of neurons within the brain remains largely unknown, and popular deep learning algorithms lack theoretical justification or reliability guarantees.  In this talk, we consider paths towards a more rigorous understanding of neural networks. We characterize and, where possible, prove essential properties of neural algorithms: expressivity, learning, and robustness. We show how observed emergent behavior can arise from network dynamics, and we develop algorithms for learning more about the network structure of the brain.

Tue, 05 Jun 2018

12:00 - 13:00
C3

Spambot detection and polarization analysis: evidence from the Italian election Twitter data

Carolina Becatti
(IMT School for Advanced Studies Lucca)
Abstract

Fake accounts detection and users’ polarization are two very well known topics concerning the social media sphere, that have been extensively discussed and analyzed, both in the academic literature and in everyday life. Social bots are autonomous accounts that are explicitly created to increase the number of followers of a target user, in order to inflate its visibility and consensus in a social media context. For this reason, a great variety of methods for their detection have been proposed and tested. Polarisation, also known as confirmation bias, is instead the common tendency to look for information that confirms one's preexisting beliefs, while ignoring opposite ones. Within this environment, groups of individuals characterized by the same system of beliefs are very likely to form. In the present talk we will first review part of the literature discussing both these topics. Then we will focus on a new dataset collecting tweets from the last Italian parliament elections in 2018 and some preliminary results will be discussed.

A new mathematical award has been established in Hungary to honour the memory of talented Hungarian mathematician András Gács (1969-2009), a man famed for his popularity among students and his capacity to inspire the young. The committee of the András Gács Award aimed to reward young mathematicians (under the age of 46), who not only excelled in research, but also motivated students to pursue mathematics.

Tue, 22 May 2018

12:30 - 13:30
C3

Cascade-Recovery Dynamics on Complex Networks

Nanxin Wei
(Department of Mathematics, Imperial College London)
Abstract


Cascading phenomena are prevalent in natural and social-technical complex networks. We study the persistent cascade-recovery dynamics on random networks which are robust against small trigger but may collapse for larger one. It is observed that depending on the relative intensity of triggering and recovery, the network belongs one of the two dynamical phases: collapsing or active phase. We devise an analytical framework which characterizes not only the critical behaviour but also the temporal evolution of network activity in both phases. Results from agent-based simulations show good agreement with theoretical calculations. This work is an important attempt in understanding networked systems gradually evolving into a state of critical transition, with many potential applications.
 

Tue, 29 May 2018
15:45
L4

Frobenius splittings of toric varieties

Milena Hering
(Edinburgh)
Abstract



Varieties admitting Frobenius splittings exhibit very nice properties.
For example, many nice properties of toric varieties can be deduced from
the fact that they are Frobenius split. Varieties admitting a diagonal
splitting exhibit even nicer properties. In this talk I will give an
overview over the consequences of the existence of such splittings and
then discuss criteria for toric varieties to be diagonally split.

Wed, 02 May 2018

16:00 - 17:00
C5

Treating vertex transitive graphs like groups

Alexander Wendland
(University of Warwick)
Abstract

In 2012 Eskin, Fisher and Whyte proved there was a locally finite vertex transitive graph which was not quasi-isometric to any connected locally finite Cayley Graph. This motivates the study of vertex transitive graphs from a geometric group theory point of view. We will discus how concepts and problems from group theory generalise to this setting. Constructing one framework in which problems can be framed so that techniques from group theory can be applied. This is work in progress with Agelos Georgakopoulos.

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