The interactions between the elementary particles are encoded into a set of mathematical quantities called scattering amplitudes. Consequently, they are key to making predictions for physical observables that match the precision achieved by current and future high-energy experiments. Due to our ignore of the mathematics involved, computing loop quantum corrections to scattering amplitudes is still a major challenge today, and calls for innovative and groundbreaking new techniques. Over the last decade, a new field of research that studies scattering amplitudes through the lens of a certain branch of modern mathematics, the so-called theory of motives, has led to breakthroughs in how we compute loop quantum corrections. LoCoMotive will bring the connection between scattering amplitudes and modern mathematics to the next level. It will investigate in detail what the theory of motives teaches us about the structure of scattering amplitudes. Its final aim is to achieve a global change of perspective on the mathematical underpinnings of the laws of nature and develop novel computational techniques for scattering amplitudes that are currently beyond reach of conventional state-of-the-art technology. Inspired by cutting-edge research in seemingly-disconnected areas in mathematics and physics, LoCoMotive will 1) perform the computations needed to reveal how concepts from geometry govern the fundamental interactions. 2) play a decisive role in providing the theoretical predictions needed for the LHC and future collider experiments. 3) act as a catalyser for new research in mathematics. To sum up, LoCoMotive is a timely proposal with a unique multi-disciplinary character, whose results will bridge a gap between formal theory and concrete phenomenological results. It will have a major impact on formal aspects of quantum field theory and possibly even pure mathematics, and provide highly-needed theoretical predictions for the LHC experiments.

Quantum field theory (QFT) is the formalism that underlies modern particle and condensed matter physics. Standard perturbative methods in QFT have been extraordinarily successful in explaining physical phenomena involving weakly-interacting quantum fields. On the other hand many fundamental phenomena, including phase transitions and nuclear interactions, are described by strongly coupled QFTs for which perturbative techniques are insufficient and a rigorous, predictive theoretical formulation is lacking. Heuristic arguments indicate that a full non-perturbative formulation of QFT must include extended degrees of freedom (a prototypical example being the flux tubes that bind quarks inside the nucleus). My proposal describes a novel approach for studying extended objects in a wide range of QFTs, based on two recent conceptual breakthroughs: first, my research on a special class of theories (the six-dimensional SCFTs) has brought to light a rich algebraic structure that captures the properties of its stringlike excitations; and second, new developments in mathematics and physics point to the existence of a vast generalization of this structure, which is perfectly suited to describe the extended objects of a much wider range of QFTs. This program is organized along three directions: analyze the families of QFTs that can be studied by string-theoretic and geometric methods, and gradually uncover the algebraic structures that describe their extended degrees of freedom; exploit these algebraic structures to obtain novel principles that govern the dynamics of strongly-interacting QFTs; and determine the new mathematical structures that arise from the combination of the geometric and algebraic description of the extended objects. An ERC starting grant will allow me to undertake this ambitious project whose pursuit will lead to a much deeper understanding of extended degrees of freedom, or their role in QFT, and of the mathematical structures that describe them.

Households face large idiosyncratic income risks and use their wealth to self insure. In doing so, they make portfolio choices we can summarize grosso modo as choices between liquid (safe and nominal) and illiquid (risky and real) assets. These choices have the potential to create strong aggregate repercussions as investments in real assets create an immediate demand for goods, while liquid nominal savings only when someone else uses the funds to invest or consume. As a result, portfolio choices are key for economic dynamics and important for the propagation of monetary and fiscal policy. Moreover, household portfolio positions and the liquidity of assets itself become an important determinant of aggregate savings and investment. Yet, they are widely disregarded in standard business cycle models today. The proposed research therefore develops a novel framework that allows us to understand this nexus--a framework that studies business cycles, household portfolios, income risks, and asset liquidity in unison. This new framework allows us to address a wide array of important macroeconomic questions of our time: how wealth inequality and stabilization policies interact, how monetary policy redistributes, how a housing freeze can create a recession as big as the last one, and finally, why crises are particularly severe in times of high household debt. To develop this framework, empirical and theoretical work has to go hand in hand: First, I document the historical movements in the distribution of household (and firm) portfolios to understand how and whose portfolio positions change over the cycle and in response to shocks. Second, I document the cyclical movements in asset liquidity. Third, I develop a theoretical framework that allows us to understand the implications of changes in asset liquidity in a setup with incomplete markets and nominal rigidities. Finally, I make liquidity fluctuations endogenous and augment the model with a structure of overlapping generations.