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## Proceedings of Journees 2019

Journees 2019 have been marked by record numbers of participants and communications. Therewere 118 attendants coming from 21 countries over the 5 continents. The scientific programincluded 58 oral presentations and 38 posters. Presentations were split into five sessions, alternatingastrometry (sessions I and III), Earth rotation changes (Session II/IV) and solar system dynamics(session V). Of particular interest were the communications dedicated to the results of the Gaiamission and its possible future prolongation in IR band (Session I), the realization of the InternationalCelestial Frame III (session III). In session II, many interesting talks were devoted to the centennialof the ”Earth rotation” IAU commission

The works that we carried out during the last ten years lead to significant progress inthe knowledge of the Chandler wobble (CW) of the Earth polar motion (PM). In Zotov and Bizouard(2012) we reconstructed the excitation of this resonant mode by using Panteleev’s correctivefiltering. Now we are sure, that this filtering is a regularizing algorithm asfar as its parameters areconsistently selected with the uncertainty affecting the resonance parameters and the observations.The excitation demonstrated a quasi 20-year amplitude modulation. In theframework of the firstorder differential linear equation describing the polar motion, it is easyto show that this modulationaccounts for the 40-year change of the CW amplitude as well as the splitting ofthe CW spectra.A simple model of the CW, composed of 80 and 40-year harmonics, accounts for the presentminimum in Chandler wobble amplitude, like in 1930s, and also predicts that its amplitude will startto increase in the nearest future with a phase shift ofπ. On the other hand, geodetic excitationof the CW well matches the ocean-atmospheric excitation (Bizouard, 2020) over recent 50 yearswith a dominant role of the ocean, producing the 20-year modulation. Thus, thephysical cause ofit could stem from climatic or tidal process influencing the oceanic circulation.

The decadal instabilities in Earth’s rotation (DIER) are thought to be caused bythe interactions between the Earth’s core and its mantle. This hypothesissuccessfully explains whythere is a close correlation between DIER and the variations in the rate of the westward drift of thegeomagnetic eccentric dipole, since it is successfully reproduced by modeling of the redistribution ofthe angular momentum between the fluid core and the mantle of the Earth. However, the hypothesiscan not explain the close correlations of DIER: with the observable variations in the masses of theAntarctic and Greenland ice sheets; with the decade oscillations of thetypes of synoptic processes(i.e. the epochs of the atmospheric circulation); with the anomalies ofthe global temperature;and with regional anomalies of the cloudiness, precipitations, and otherclimatic characteristics. Analternative to the core-mantle interaction hypothesis is presentedhere. This alternative hypothesisclaims that the DIER are actually caused by fluctuations in the angular velocity of lithospheric driftover the asthenosphere. The sliding of the lithosphere over the asthenosphere is possible due to ofthe vibrational displacement mechanism produced by tidal forces. The lithospheric plates exhibitvibrational displacements over the asthenosphere in the horizontal direction by shear stresses causedby friction, wind, and ocean currents. There is abundant evidence supporting thislithospheric driftmodel.

This study investigates the relationship between the equatorial atmospheric angular mo- mentum oscillation in the non-rotating frame and lunar tidal potential. Between 2 and 30 days, the corresponding equatorial component is mostly constituted of prograde circular motions, especially of a harmonic at 13.6 days, and of a weekly broad band variation. A simple equilibrium tide model explains the 13.6-day pressure term as result of the lunar tide; the tidal lunar origin of the whole band from 2 to 30 days is attested by speciØc features, not occurring for seasonal band dominated by the solar thermal effect

Observed polar motion consists of uniform circular motions at both positive (prograde) and negative (retrograde) frequencies. Generalized Euler–Liouville equations of Bizouard, taking into account Earth's triaxiality and asymmetry of the ocean tide, show that the corresponding retrograde and prograde circular excitations are coupled at any frequency. In this work, we reconstructed the polar motion excitation in the Chandler band (prograde and retrograde). Then we compared it with geophysical excitation, filtered out in the same way from the series of the Oceanic Angular Momentum (OAM) and Atmospheric Angular Momentum (AAM) for the period 1960–2000. The agreement was found to be better in the prograde band than in the retrograde one.

Chandler wobble amplitude have been decreasing in 2010s as in 1930s. We try to predict its future behaviour through prediction of its complex envelope. The excitation of the Chandler wobble (ChW) reconstructed by Panteleev's ¯lter was also analized. The equation for the complex envelope propagation through the Euler-Liouville equation was derived. Similarities with the climate change characteristics are discussed.

From the maps of regional contribution to atmospheric angular momentum (AAM) over the period 1948–2011 (NCEP/NCAR reanalysis data) time domain excitation in Chandler frequency band was extracted by Panteleev’s filtering method. This permits us to investigate the evolution of the regional atmospheric influence on Chandler wobble. It appears that the temperate latitudes bring the strongest inputs. For pressure term they are limited to continents, and highlight the role of Europe. For the wind term they mostly result from ocean area, encompassing in particular North Atlantic. A quasi-20 year cycle is found in the regional patterns of the atmospheric excitation. The integrated AAM is finally compared with the geodetic excitation reconstructed from the observed polar motion.

Multichannel singular spectrum analysis (MSSA) is applied to the globally gridded oceanic angular momentum (OAM) data from ECCO (KF080) model, Atmospheric Angular Momentum from ECMWF model, and Earth gravity field from GRACE satellites. Principal components of the oceanic, atmospheric, and hydrological changes and their influence on the rotation of the Earth (polar motion PM and length of day LOD) are extracted. The regions where mass and motion terms make the largest input into PM excitation and LOD changes are identified. The trends, annual, and other global-scale modes are separated. Multichannel singular spectrum analysis is found to be a promising method for signal filtering and modes decomposition. Possible connections between climate change and Earth rotation are discussed.

This study investigates the relationship between the equatorial atmospheric angular momentum oscillation in the nonrotating frame and the quasi-diurnal lunar tidal potential. Between 2 and 30 days, the corresponding equatorial component, called Celestial Atmospheric Angular Momentum (CEAM), is mostly constituted of prograde circular motions, especially of a harmonic at 13.66 days, a sidelobe at 13.63 days, and of a weekly broadband variation. A simple equilibrium tide model explains the 13.66 day pressure term as a result of the O1 lunar tide. The powerful episodic fluctuations between 5 and 8 days possibly reflect an atmospheric normal mode excited by the tidal waves Q1 (6.86 days) and *σ*1 (7.095 days). The lunar tidal influence on the spectral band from 2 to 30 days is confirmed by two specific features, not occurring for seasonal band dominated by the solar thermal effect. First, Northern and Southern Hemispheres contribute equally and synchronously to the CEAM wind term. Second, the pressure and wind terms are proportional, which follows from angular momentum budget considerations where the topographic and friction torques on the solid Earth are much smaller than the one resulting from the equatorial bulge. Such a configuration is expected for the case of tidally induced circulation, where the surface pressure variation is tesseral and cannot contribute to the topographic torque, and tidal winds blow only at high altitudes. The likely effects of the lunar-driven atmospheric circulation on Earth's nutation are estimated and discussed in light of the present-day capabilities of space geodetic techniques.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.